Remarks on some nonlinear Dirichlet problems with unbounded nonlinearities

Juan J. Nieto

Commentationes Mathematicae Universitatis Carolinae (1990)

  • Volume: 031, Issue: 3, page 511-515
  • ISSN: 0010-2628

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Nieto, Juan J.. "Remarks on some nonlinear Dirichlet problems with unbounded nonlinearities." Commentationes Mathematicae Universitatis Carolinae 031.3 (1990): 511-515. <http://eudml.org/doc/17873>.

@article{Nieto1990,
author = {Nieto, Juan J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {duality principle; alternative method; Dirichlet problem},
language = {eng},
number = {3},
pages = {511-515},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Remarks on some nonlinear Dirichlet problems with unbounded nonlinearities},
url = {http://eudml.org/doc/17873},
volume = {031},
year = {1990},
}

TY - JOUR
AU - Nieto, Juan J.
TI - Remarks on some nonlinear Dirichlet problems with unbounded nonlinearities
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1990
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 031
IS - 3
SP - 511
EP - 515
LA - eng
KW - duality principle; alternative method; Dirichlet problem
UR - http://eudml.org/doc/17873
ER -

References

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  1. Aguinaldo L., Schmitt K., On the boundary value problem u " + u = a u - + p ( t ) , u ( 0 ) = 0 = u ( π ) , Proc. Amer. Math. Soc. 68 (1978), 64-68. (1978) Zbl0385.34005MR0466707
  2. Ahmad S., A resonance problem in which the nonlineariiy may grow linearly, Proc. Amer. Mat. Soc. 82 (1984), 381-384. (1984) MR0759657
  3. Brezis H., Periodic solutions of nonlinear vibrating strings and duality principles, Bull. Amer. Math. Soc. 8 (1983), 409-426. (1983) Zbl0537.35055MR0693957
  4. Cesari L., Kannan R., An abstract theorem at resonance, Proc. Amer. Math. Soc. 63 (1977), 221-225. (1977) Zbl0361.47021MR0448180
  5. Cesari L., Kannan R., Existence of solutions of a nonlinear differential equation, Proc. Amer. Math. Soc. 88 (1983), 605-613. (1983) Zbl0529.34005MR0702284
  6. Drábek P., On the resonance problem with nonlinearity which has arbitrary linear growth, J. Math. Anal. Appl. 127 (1987), 435-442. (1987) Zbl0642.34009MR0915069
  7. Fučík S., Boundary value problems with jumping nonlinearities, Časopis Pěst. Mat. 101 (1976), 69-87. (1976) Zbl0332.34016MR0447688
  8. Iaanaci R., Nkashama M.N., Ward J.R., Nonlinear second order elliptic partial differential equations at resonance, Trans. Amer. Math. Soc. 311 (1989), 711-726. (1989) MR0951886
  9. Kannan R., Ortega R., Existence of solutions of x ' ' + x + g ( x ) = p ( t ) , x ( 0 ) = 0 = x ( π ) , Proc. Amer. Math. Soc. 96 (1986), 67-70. (1986) Zbl0585.34001MR0813812
  10. Kannan R., Lakshmikantham V., Nieto J. J., Sufficient conditions for existence of solutions of nonlinear boundary value problems at resonance, Nonlinear Anal. 7 (1983), 1013-1020. (1983) Zbl0542.47053MR0713210
  11. Kannan R., Nieto J. J., Ray M. B., A class of nonlinear boundary value problems without Landesman-Lazer condition, J. Math. Anal. Appl. 105 (1985), 1-11. (1985) Zbl0589.34013MR0773569
  12. Nieto J. J., Hukuhara-Kneser property for a nonlinear Dirichlet problem, J. Math. Anal. Appl. 128 (1987), 57-63. (1987) Zbl0648.34019MR0915966
  13. Nieto J. J., Aronszajn's theorem for some nonlinear Dirichlet problems with unbounded nonlinearities, Proc. Edinburgh Math. Soc. 31 (1988), 345-351. (1988) Zbl0631.34027MR0969064
  14. Schechter M., Shapiro J., Snow M., Solutions of the nonlinear problem A u = N u in a Banach space, Trans. Amer. Math. Soc. 241 (1978), 69-78. (1978) MR0492290

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