Landesman-Lazer type condition and nonlinearities with linear growth

Pavel Drábek

Czechoslovak Mathematical Journal (1990)

  • Volume: 40, Issue: 1, page 70-86
  • ISSN: 0011-4642

How to cite

top

Drábek, Pavel. "Landesman-Lazer type condition and nonlinearities with linear growth." Czechoslovak Mathematical Journal 40.1 (1990): 70-86. <http://eudml.org/doc/13831>.

@article{Drábek1990,
author = {Drábek, Pavel},
journal = {Czechoslovak Mathematical Journal},
keywords = {Leray-Schauder degree theory; jumping nonlinearities; semilinear boundary value problems with nonlinearities; solvability},
language = {eng},
number = {1},
pages = {70-86},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Landesman-Lazer type condition and nonlinearities with linear growth},
url = {http://eudml.org/doc/13831},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Drábek, Pavel
TI - Landesman-Lazer type condition and nonlinearities with linear growth
JO - Czechoslovak Mathematical Journal
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 1
SP - 70
EP - 86
LA - eng
KW - Leray-Schauder degree theory; jumping nonlinearities; semilinear boundary value problems with nonlinearities; solvability
UR - http://eudml.org/doc/13831
ER -

References

top
  1. S. Ahmad, 10.1090/S0002-9939-1984-0759657-9, Proc. Amer. Math. Soc. 93 (1984), 381-384. (1984) MR0759657DOI10.1090/S0002-9939-1984-0759657-9
  2. S. Ahmad, 10.1016/0362-546X(86)90042-8, Nonlinear Analysis 10 (1986), 147-156. (1986) Zbl0599.35069MR0825213DOI10.1016/0362-546X(86)90042-8
  3. S. Ahmad A. C. Lazer, Critical point theory and a theorem of Amaral and Pera, Boll. Un. Mat. Ital. 3-B (1984), 583-598. (1984) MR0774464
  4. M. Arias, 10.1090/S0002-9939-1986-0831399-2, Proc. Amer. Math. Soc. 97 (1986), 121-127. (1986) Zbl0595.34017MR0831399DOI10.1090/S0002-9939-1986-0831399-2
  5. M. d'Aujourd'hui, 10.1016/0362-546X(87)90062-9, Nonlinear Analysis 11 (1987), 969-977. (1987) Zbl0641.34020MR0903788DOI10.1016/0362-546X(87)90062-9
  6. M. d'Aujourd'hui, Problèmes aux limites elliptiques demilinéaires, Thése No 692 (1987), Ecole Polytechnique Federale de Lausanne, pp. 127. (1987) 
  7. M. d'Aujourd'hui, The stability of the resonance set for a problem with jumping nonlinearity, to appear in Proc. Roy. Soc. Edinb. 1987. (1987) Zbl0704.34010MR0924517
  8. M. d'Aujourd'hui, On the number of solutions of some semilinear boundary value problems, Equadiff Conference 87. Zbl0704.35049
  9. A.Bahri H. Berestycki, Points critiques de perturbations de functionelles paires et applications, C. R. Acad. Sci. Paris Sér. A-B 291 (1980), A 189-A 192. (1980) MR0594288
  10. A. Bahri H. Berestycki, 10.1090/S0002-9947-1981-0621969-9, Trans. Amer. Math. Society 267 (1981), 1 - 32. (1981) MR0621969DOI10.1090/S0002-9947-1981-0621969-9
  11. H. Berestycki D. G. deFigueiredo, 10.1080/03605308108820172, Comm. Partial Differential Equations 6 (1981), 91-120. (1981) MR0597753DOI10.1080/03605308108820172
  12. H. Brézis, Semilinear equations in R n without condition at infinity, Appl. Math. Optim. (to appear). MR0768633
  13. A. Canada, 10.1016/0022-247X(86)90244-1, J. Math. Anal. Applications 117 (1986), 1 - 22. (1986) Zbl0604.34012MR0843001DOI10.1016/0022-247X(86)90244-1
  14. A. Canada P. Martines-Amores, 10.1016/0022-0396(83)90004-9, J. Differential Equations 48 (1983), 415-429. (1983) MR0715694DOI10.1016/0022-0396(83)90004-9
  15. A. Canada P. Martines-Amores, 10.1016/0362-546X(83)90031-7, Nonlinear Analysis 7 (1983), 747-761. (1983) MR0707083DOI10.1016/0362-546X(83)90031-7
  16. A. Canada R. Ortega, Existence theorems for equations in normed spaces and nonlinear boundary-value problems for nonlinear vector ordinary differential equations, Proc. Roy. Soc. Edinburgh 98A (1984), 1-11. (1984) MR0765484
  17. A. Castro, 10.1090/S0002-9939-1980-0565340-1, Proc. Amer. Math. Soc. 79 (1980), 207-211. (1980) Zbl0439.34021MR0565340DOI10.1090/S0002-9939-1980-0565340-1
  18. G. Caristi, 10.1016/0362-546X(87)90112-X, Nonlinear Analysis 11 (1987), 851 - 860. (1987) MR0898579DOI10.1016/0362-546X(87)90112-X
  19. G. Caristi, On periodic solutions of systems of coupled pendulum-like equations, preprint (Trieste). 
  20. G. Caristi, Periodic solutions of bounded perturbations of linear second order ordinary differential systems, preprint (Trieste). Zbl0664.34048MR1068871
  21. L. Cesari R. Kannan, 10.1016/0022-0396(85)90100-7, J. Differential Equations 56 (1985), 63-81. (1985) MR0772121DOI10.1016/0022-0396(85)90100-7
  22. K. C. Chang, A variant mountain pass lemma, Sci. Sinica Ser. A (1983), 1241-1255. (1983) Zbl0544.35044MR0745796
  23. K. C. Chang, Variational methods and sub and super-solutions, Sci. Sinica Ser. A 26 (1983), 1256-1265. (1983) Zbl0544.35045MR0745797
  24. R. Chiappinelli J. Mawhin R. Nugari, 10.1016/0022-0396(87)90127-6, J. Differential Equations 69 (1987), 422-434. (1987) MR0903395DOI10.1016/0022-0396(87)90127-6
  25. R. Conti R. Iannacci M. N. Nkashama, Periodic solutions of Lienard systems at resonance, Ann. Math. Pura Appl. (4) 139 (1985), 313-328. (1985) MR0798178
  26. D. G. Costa D. G. deFigueiredo J. V. A. Consalves, 10.1016/0022-247X(87)90302-7, J. Math. Anal. Appl. 123 (1987), 170-180. (1987) MR0881539DOI10.1016/0022-247X(87)90302-7
  27. E. N. Dancer, 10.1007/BF01765151, Ann. Math. Pura Appl. 4 (1982), 167-185. (1982) Zbl0519.34011MR0681562DOI10.1007/BF01765151
  28. E. N. Dancer, 10.1007/BF01455568, Math. Ann 272 (1985), 421 - 440. (1985) MR0799671DOI10.1007/BF01455568
  29. T. R. Ding, Some fixed point theorems and periodically perturbed nondissipative systems, Chinese Ann. Math. 2 (3) (1981), 281 - 300. (1981) Zbl0484.34025MR0670138
  30. T. R. Ding, 10.1090/S0002-9939-1982-0663864-1, Proc. Amer. Math. Society 86 (1982), 47-54. (1982) Zbl0511.34031MR0663864DOI10.1090/S0002-9939-1982-0663864-1
  31. T. R. Ding, Nonlinear oscillations at a point of resonance, Sci. Sinica Ser A 25 (9) (1982), 918-931. (1982) Zbl0509.34043MR0681856
  32. T. R. Ding, 10.1090/S0002-9939-1983-0691279-X, Proc. Amer. Math. Society (1) 88 (1983), 59-66. (1983) Zbl0538.34028MR0691279DOI10.1090/S0002-9939-1983-0691279-X
  33. P. Drábek, Solvability of the superlinear elliptic boundary value problem, Comment. Math. Univ. Carolinae 22 (1981), 27-35. (1981) MR0609934
  34. P. Drábek, Bounded nonlinear perturbations of second order linear elliptic problems, Comment. Math. Univ. Carolinae 22 (1981), 215-221. (1981) MR0620358
  35. P. Drábek, Solvability of nonlinear problems at resonance, Comment. Math. Univ. Carolinae 23 (1982), 359-367. (1982) MR0664981
  36. P. Drábek, Existence and multiplicity results for some weakly nonlinear elliptic problems at resonance, Čas. pěst. mat. 108 (1983), 272-284. (1983) MR0716412
  37. P. Drábek, 10.1016/0022-247X(87)90121-1, J. Math. Anal. Applications 127 (1987), 435-442. (1987) MR0915069DOI10.1016/0022-247X(87)90121-1
  38. P. Drábek, A resonance problem for nonlinear Duffing equation, Comment. Math. Univ. Carolinae 29 (1988), 205-215. (1988) MR0957386
  39. P. Drábek, Landesman-Lazer condition for nonlinear problems with jumping nonlinearities, to appear. MR1052334
  40. P. Drábek S. Invernizzi, Periodic solutions for systems of forced coupled pendulum-like equations, J. Differential Equations 76 (1987), 390-402. (1987) MR0915495
  41. P. Drábek S. A. Tersian, 10.1016/0362-546X(87)90039-3, Nonlinear Analysis 11 (1987), 733 - 739. (1987) MR0893777DOI10.1016/0362-546X(87)90039-3
  42. N. Dunford J. T. Schwartz, Linear Operators. Part I, Interscience Publ., New York, 1958. (1958) MR0117523
  43. C. Fabry J. Mawhin M. N. Nkashama, 10.1112/blms/18.2.173, Bull. London Math. Soc. 18 (1986), 173-180. (1986) MR0818822DOI10.1112/blms/18.2.173
  44. M. C. L. Fernandes P. Omari F. Zanolin, On the solvability of a semilinear two-point BVP around the first eigenvalue, Preprint 77/87/M, SISSA, Trieste 1987. (1987) 
  45. M. C. L. Fernandes F. Zanolin, Periodic solutions of a second order differential equation with one-sided growth restrictions on the restoring term, Preprint 43/87/M, SISSA, Trieste 1987. (1987) MR0959391
  46. D. G. deFigueiredo, Semilinear elliptic equations at resonance: Higher eigenvalues and unbounded nonlinearities, in: Recent Advance in Differential Equations (R. Conti Ed.) pp. 89 - 99, Academic Press, London 1981. (1981) MR0643128
  47. D. G. deFigueiredo, On the superlinear Ambrosetti-Prodi problem, Nonlinear Analysis 5 (1984), 655-666. (1984) MR0746723
  48. D. G. deFigueiredo, 10.1016/0362-546X(87)90066-6, Nonlinear Analysis 11 (1987), 481-492. (1987) MR0887657DOI10.1016/0362-546X(87)90066-6
  49. D. G. deFigueiredo S. Solimini, 10.1080/03605308408820345, Comm. Partial Differential Equations 9 (1984), 699-717. (1984) MR0745022DOI10.1080/03605308408820345
  50. D. G. deFigueiredo W. M. Ni, Perturbations of second order linear elliptic problems by nonlinearities without Landesman-Lazer condition, Nonlinear Analysis 5 (1981), 57-60. (1981) 
  51. D. Fortunato E. Jannelli, Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains, Proc. Royal Soc. Edinburgh 105A (1987), 205-213. (1987) MR0890056
  52. G. Fournier J. Mawhin, On periodic solutions of forced pendulum-like equations, Sémin. de Math. No 48, UCL, Louvain-la-Neuve, 1984. (1984) MR0811773
  53. S. Fučík, Solvability of Nonlinear Equations and Boundary Value Problems, D. Reidel Publ. Company, Holland 1980. (1980) MR0620638
  54. T. Gallouët 0. Kavian, Résultats d'Existence et de Non-Existence pour certains Problèmes Demilineaires a l'infini, Ann. Fac. Sc. de Toulouse 1981. (1981) 
  55. T. Gallouët O. Kavian, 10.1080/03605308208820225, Comm. Part. Diff. Equations 7 (3) (1982), 325-342. (1982) MR0646710DOI10.1080/03605308208820225
  56. T. Gallouët J. M. Morel, The equation - Δ u + | u | α - 1 u = f , for 0 α 1 , Nonlinear Analysis 11 (1987), 893-912. (1987) MR0903785
  57. C. P. Gupta, 10.1016/0362-546X(82)90011-6, Nonlinear Analysis 6 (1982), 919-933. (1982) Zbl0509.35035MR0677617DOI10.1016/0362-546X(82)90011-6
  58. P. Habets M. N. Nkashama, On periodic solutions of nonlinear second order vector differential equations, Proc. Roy. Soc. Edinburgh 104A (1986), 107-125. (1986) MR0877895
  59. D. C. Hart A. C. Lazer P. J. McKenna, 10.1016/0022-0396(85)90158-5, J. Differential Equations 59 (1985), 266-281. (1985) MR0804892DOI10.1016/0022-0396(85)90158-5
  60. H. Hofer, 10.1007/BF01457453, Math. Ann. 267 (1982), 493-514. (1982) Zbl0488.47034MR0682663DOI10.1007/BF01457453
  61. R. Iannacci M. N. Nkashama, 10.1016/0362-546X(87)90064-2, Nonlinear Analysis 11 (1987), 455-474. (1987) MR0887655DOI10.1016/0362-546X(87)90064-2
  62. R. Iannacci M. N. Nkashama, 10.1016/0022-0396(87)90121-5, J. Differential Equations 69 (1987), 289-309. (1987) MR0903389DOI10.1016/0022-0396(87)90121-5
  63. R. Iannacci M. N. Nkashama P. Omari F. Zanolin, Periodic solutions with jumping nonlinearities under nonuniform conditions, to appear. 
  64. R. Iannacci M. N. Nkashama J. R. Ward, Nonlinear second order elliptic partial differential equations at resonance, preprint Memphis State University, Dept. of Mathematics 1987. (1987) 
  65. S. Invernizzi, A note on nonuniform nonresonance for jumping nonlinearities, Comment. Math. Univ. Carolinae 27 (1986), 285-291. (1986) Zbl0603.34016MR0857548
  66. R. Kannan V. Lakshmikantham J. J. Nieto, 10.1016/0362-546X(83)90116-5, Nonlinear Analysis 7 (1983), 1013-1020. (1983) MR0713210DOI10.1016/0362-546X(83)90116-5
  67. R. Kannan R. Ortega, 10.1016/0022-0396(85)90141-X, J. Differential Equations 59 (1985), 123-144. (1985) MR0803090DOI10.1016/0022-0396(85)90141-X
  68. R. Kannan R. Ortega, 10.1080/00036818608839604, Applicable Analysis 22 (1986), 45-53. (1986) MR0854539DOI10.1080/00036818608839604
  69. R. Kannan R. Ortega, Superlinear elliptic boundary value problems, Czech. Math. J. 37 (1987), 386-399. (1987) MR0904766
  70. R. Kent Nagle K. Singhofer, 10.1080/00036818008839327, Applicable Analysis 11 (1980), 137-149. (1980) MR0599262DOI10.1080/00036818008839327
  71. R. Kent Nagle K. Singhofer, 10.1016/0022-247X(83)90015-X, J. Math. Analysis Appl. 94 (1983), 222-236. (1983) MR0701459DOI10.1016/0022-247X(83)90015-X
  72. E. M. Landesman A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609 - 623. (1970) MR0267269
  73. A. C. Lazer D. E. Leach, Bounded perturbations of forced harmonic oscillators at resonance, Ann. Math. Pura Appl. (4) 82 (1969), 49-68. (1969) MR0249731
  74. A. C. Lazer P. J. McKenna, 10.1016/0022-247X(81)90166-9, J. Math. Anal. Appl. 84 (1981), 282-294. (1981) MR0639539DOI10.1016/0022-247X(81)90166-9
  75. A. C. Lazer P. J. McKenna, On limitations to the solution set of some nonlinear problems, in: Dynamical systems II pp. 247-253, Academic Press, New York-London, 1982. (1982) MR0703698
  76. A. C. Lazer P. J. McKenna, On a conjecture on the number of solutions of a nonlinear Dirichlet problem with jumping nonlinearity, in: Trends in theory and practice of nonlinear differential equations (Arlington, Texas 1982) pp. 301 - 313, Lecture Notes in Pure and Appl Math. 90, Dekker New York, 1984. (1982) MR0741517
  77. A. C. Lazer P. J. McKenna, On a conjecture related to the number of solutions of a nonlinear Dirichlet problem, Proc. Royal Soc. Edinburgh Sect. 1 95 (1983), 275-283. (1983) MR0726879
  78. A. C. Lazer P. J. McKenna, Recent multiplicity results for nonlinear boundary value problems, in: Differential equations (Birmingham, Ala., 1983), pp. 391 - 396, NorthHolland, Amsterdam-New York, 1984. (1983) MR0799375
  79. A. C. Lazer P. J. McKenna, 10.1016/0022-247X(85)90320-8, J. Math. Anal. Appl. 107 (1985), 371 - 395. (1985) MR0787722DOI10.1016/0022-247X(85)90320-8
  80. A. C. Lazer P. J. McKenna, 10.1016/0362-546X(85)90058-6, Nonlinear Analysis 9 (1985), 335-350. (1985) MR0783582DOI10.1016/0362-546X(85)90058-6
  81. A. C. Lazer P. J. McKenna, 10.1080/03605308508820374, Comm. Partial Differential Equations 10 (1985), 107-150. (1985) MR0777047DOI10.1080/03605308508820374
  82. D. Lupo S. Solimini, A note on a resonance problem, preprint. MR0837156
  83. J. Mawhin, Compacité, monotonie et convexité dans Pétude des problèmes aux limites semi-linéaires, Sémin. d'Analyse Moderne No. 19, Université de Sherbrooke, 1981. (19,) 
  84. J. Mawhin, 10.1007/BFb0065017, in: Ordinary and Partial Differential Equations, Lecture Notes in Mathematics no. 964, pp. 458-476, Springer-Verlag, Berlin-New York, 1982. (1982) Zbl0517.34029MR0693131DOI10.1007/BFb0065017
  85. J. Mawhin, Boundary value problems with nonlinearities having infinite jumps, Comment. Math. Univ. Carolinae 25 (1984), 401-414. (1984) Zbl0562.34010MR0775560
  86. J. Mawhin J. R. Ward, 10.1007/BF01371406, Arch. Math. 41 (1983), 337-351. (1983) MR0731606DOI10.1007/BF01371406
  87. J. Mawhin W. Willem, 10.1016/0022-0396(84)90180-3, J. Differential Equations 52 (1984), 264-287. (1984) MR0741271DOI10.1016/0022-0396(84)90180-3
  88. P. J. McKenna R. Redlinger W. Walter, 10.1007/BF01769219, Ann. Math. Pura Appl. 143 (1986), 247-258. (1986) MR0859606DOI10.1007/BF01769219
  89. P. S. Milojevic, 10.1080/00036818708839684, Applicable Analysis 25 (1987), 181-196. (1987) MR0912180DOI10.1080/00036818708839684
  90. M. N. Nkashama, Solutions périodiques des systèmes non conservatifs périodiquement perturbés, Bull. Soc. Math. France 113 (1985), 387-402. (1985) Zbl0607.34041MR0850775
  91. M. N. Nkashama, Periodically perturbed nonconservative systems of Liénard type, preprint Memphis State University, Department of Mathematics 1987. (1987) MR1057959
  92. P. Omari G. Villari F. Zanolin, 10.1016/0022-0396(87)90151-3, J. Differential Equations 67 (1987), 278 - 293. (1987) MR0879698DOI10.1016/0022-0396(87)90151-3
  93. P. Omari F. Zanolin, 10.1007/BF01763171, Ann. Math. Pura Appl. 141 (1985), 127-157. (1985) MR0816782DOI10.1007/BF01763171
  94. P. Omari F. Zanolin, Some remarks about the paper "Periodic solutions of the Liénard equation with one sided growth restrictions", (unpublished internal report), Trieste 1986. (1986) 
  95. P. Omari F. Zanolin, 10.1016/0362-546X(87)90104-0, Nonlinear Analysis 11 (1987), 275-284. (1987) MR0877887DOI10.1016/0362-546X(87)90104-0
  96. R. Ortega, A counterexample for the damped pendulum equation, preprint. Zbl0679.70022MR1026970
  97. W. V. Petryshyn Z. S. Yu, 10.1016/0022-247X(84)90278-6, J. Math. Anal. Appl. 98 (1984), 72 - 91. (1984) Zbl0529.34023MR0728517DOI10.1016/0022-247X(84)90278-6
  98. W. V. Petryshyn Z. S. Yu, 10.1016/0362-546X(85)90079-3, Nonlinear Analysis 9 (1985), 969 - 975. (1985) MR0804562DOI10.1016/0362-546X(85)90079-3
  99. M. Ramaswamy, 10.1016/0022-0396(86)90040-9, J. Differential Equations 65 (1987), 1 - 48. (1987) MR0859471DOI10.1016/0022-0396(86)90040-9
  100. B. Ruf, Multiplicity results for superlinear elliptic equations, Nonlinear Funct. Anal. and Appl. (Maratea, 1985), pp. 353-367, NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 173, Reidel, Dordrecht-Boston, Mass., 1986. (1985) MR0852595
  101. B. Ruf, 10.1016/0362-546X(85)90092-6, Nonlinear Analysis 9 (1985), 1325-1330. (1985) Zbl0626.34017MR0820643DOI10.1016/0362-546X(85)90092-6
  102. B. Ruf, 10.1002/mana.19861270121, Math. Nachr. 127 (1986), 299-308. (1986) Zbl0605.34020MR0861733DOI10.1002/mana.19861270121
  103. B. Ruf S. Solimini, 10.1137/0517055, SIAM J. Math. Anal. 17 (1986), 761 - 771. (1986) MR0846387DOI10.1137/0517055
  104. B. Ruf P. N. Srikanth, 10.1016/0022-247X(86)90286-6, J. Math. Anal. Appl. 118 (1986), 15-23. (1986) MR0849438DOI10.1016/0022-247X(86)90286-6
  105. B. Ruf P. N. Srikanth, 10.1016/0362-546X(86)90043-X, Nonlinear Analysis 10 (1986), 157-163. (1986) MR0825214DOI10.1016/0362-546X(86)90043-X
  106. L. Sanches, 10.1080/00036818708839691, Applicable Analysis 25 (1987), 275-286. (1987) MR0912186DOI10.1080/00036818708839691
  107. K. Schmidt, Boundary value problems with jumping nonlinearities, Rocky Mountain J. Math. 16 (1986),481-496. (1986) MR0862276
  108. S. Solimini, 10.1016/S0294-1449(16)30407-3, Ann. Inst. H. Poincaré Anal. Non Lineaire 2 (1985), 143-156. (1985) Zbl0583.35044MR0794004DOI10.1016/S0294-1449(16)30407-3
  109. S. Solimini, 10.1016/0022-247X(86)90253-2, J. Math. Anal. Appl. 117 (1986), 138-152. (1986) Zbl0634.35030MR0843010DOI10.1016/0022-247X(86)90253-2
  110. Song-Sun Lin, 10.1016/0022-247X(83)90193-2, J. Math. Analysis Appl. 93 (1983), 574-592. (1983) MR0700164DOI10.1016/0022-247X(83)90193-2
  111. H. Triebel, Mapping properties of nonlinear operators generated by Φ ( u ) = | u | ρ and by holomorphic Φ ( u ) in function spaces of Besov-Hardy-Sobolev type. Boundary value problems for elliptic differential equations of type Δ u = f ( x ) + Φ ( u ) ., Math. Nachr. 117 (1984), 193-213. (1984) Zbl0573.35032MR0755303
  112. J. R. Ward, 10.1016/0022-247X(81)90052-4, J. Math. Anal. Appl. 81 (1981), 92-98. (1981) Zbl0462.34023MR0618763DOI10.1016/0022-247X(81)90052-4
  113. J. R. Ward, 10.1090/S0002-9939-1981-0597653-2, Proc. Amer. Math. Soc. 81 (1981), 415-420. (1981) Zbl0461.34029MR0597653DOI10.1090/S0002-9939-1981-0597653-2
  114. J. R. Ward, 10.1016/0022-0396(82)90062-6, J. Differential Equations 45 (1982), 156-167. (1982) Zbl0515.34003MR0665993DOI10.1016/0022-0396(82)90062-6
  115. J. R. Ward, 10.1016/0362-546X(82)90022-0, Nonlinear Analysis 6 (1982), 367-374. (1982) Zbl0533.35033MR0654812DOI10.1016/0362-546X(82)90022-0
  116. J. R. Ward, 10.1016/0362-546X(86)90047-7, Nonlinear Analysis 10 (1986), 207-213. (1986) Zbl0609.34021MR0825218DOI10.1016/0362-546X(86)90047-7
  117. J. R. Ward, A note on the Dirichlet problem for some semilinear elliptic equations, preprint. 
  118. M. Willem, 10.1016/0362-546X(81)90100-0, Nonlinear Analysis 5 (1981), 517-524. (1981) Zbl0472.47036MR0613060DOI10.1016/0362-546X(81)90100-0
  119. S. A. Williams, 10.1016/0022-0396(70)90031-8, J. Differential Equations 8 (1970), 580-586. (1970) Zbl0209.13003MR0267267DOI10.1016/0022-0396(70)90031-8
  120. F. Zanolin, Remarks on multiple periodic solutions for nonlinear ordinary differential system of Liénard type, Boll. Un. Mat. Ital. (6) 1-B (1982), 683-698. (1982) MR0666597

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.