Characterizations of the ranges of some nonlinear operators and applications to boundary value problems

 Access to full text

 Full (PDF)

1. [A-L-P] S. Ahmad - A.C. Lazer - J.L. Paul, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. J., 25 (1976), pp. 933-944. Zbl0351.35036MR427825
2. [A-M] A. Ambrosetti - G. Mancini, Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance. - I: The case of simple eigenvalue, to appear. Zbl0393.35032MR492839
3. [Ba-Ha] J.B. Baillon - G. Haddad, Quelques propriétés des opérateurs anglebornés et n-cycliquement monotones, Israel J. Math., 26 (1977), pp. 137-150. Zbl0352.47023MR500279
4. [B-H-V] P. Baras - J.C. Hassan - L. Veron, Oompacité de l'opérateur définissant la solution d'une équation d'évolution non homogène, C. R. Acad. Sc., 284 (1977), pp. 799-802. Zbl0348.47026MR430864
5. [B-S] M. Berger - M. Schechter, On the solvability of semilinear operator equations and elliptic boundary value problems, Bull. A.M.S., 78 (1972), pp. 741-745. Zbl0263.35036MR303374
6. [Bré-1] H. Brézis, On some degenerate nonlinear parabolic equations, Nonlinear Functional Analysis, Proc. Symp. Pure Math., Vol. 18 (part 1), F. Browder ed. AMS (1970), pp. 28-38. Zbl0231.47034MR273468
7. [Bré-2] H. Brézis, Opérateurs maximaux monotones, Lecture Notes, Vol. 5, North-Holland, 1973. 
8. [B-B] H. Brézis - F. Browder, Nonlinear integral equations and systems of Hammerstein type, Advances in Math., 18 (1975), pp. 115-147. Zbl0318.45011MR394341
9. [Br-Ha] H. Brézis - A. Haraux, Image d'une somme d'opérateurs monotones et applications, Israel J. Math., 23 (1976), pp. 165-186. Zbl0323.47041MR399965
10. [Br-N] H. Brézis - L. Nirenberg, Forced vibrations for a nonlinear wave equation, Comm. Pure Appl. Math., 31 (1978). Zbl0378.35040MR470377
11. [Bro-1] F. Browder, Nonlinear Operators in Banach Spaces, Proc. Symp. Pure Math., Vol. 18 (part 2) AMS (1976). MR405188
12. [Bro-2] F. Browder, On a principte of H. Brézis and its applications, J. Funct. Anal., 25 (1977), pp. 356-365. Zbl0358.47037MR445344
13. [C-G] B. Calvert - C. Gupta, Nonlinear elliptic boundary value problems in Lp spaces and sums of ranges of accretive operators, Nonlinear Analysis, TMA2 (1978), pp. 1-26. Zbl0369.47033MR512651
14. [C] L. Cesari, Alternative methods in nonlinear analysis, International Conference on Differential Equations, Antosiewicz ed. Acad. Press. (1975). Zbl0316.47039MR430884
15. [Da-1] E.N. Dancer, On a nonlinear elliptic boundary value problem, Bull. Aust. Math. Soc., 12 (1975), pp. 399-405. Zbl0297.35031MR385318
16. [Da-2] E.N. Dancer, On the Dirichlet problem for weakly nonlinear elliptic partial differential equations, to appear. Zbl0351.35037
17. [DeF-1] D.G. De Figueiredo, The Dirichlet problem for nonlinear elliptic equations : A Hilbert space approach, Partial differential equations and related topics, Springer Verlag Lecture Notes446 (1975), pp. 144-165. Zbl0312.35032MR437924
18. [DeF-2] D.G. De Figueiredo, Semilinear elliptic problems with nonlinearities near the first eigenvalue, Proc. Symp. Dynamical Systems, Univ. of Florida (1976), to appear. Zbl0538.34013
19. [DeF-G] D.G. De Figueiredo - J.P. Gossez, Nonlinear perturbations of a linear elliptic problem near its first eigenvalues, to appear. Zbl0357.35036
20. [DeS-T] L. De Simon - G. Torelli, Soluzione periodiche di equazioni a derivate parziali di tipo iperbolico nonlineari, Rend. Sem. Math. Univ. Padova, 40 (1968), pp. 380-401. Zbl0198.13704MR228836
21. [Du] J.C. Dunn, Convexity, monotonicity and gradient processes in Hilbert space, J. Math. Anal. Applic., 53 (1976), pp. 145-158. Zbl0321.49025MR388176
22. [F-1] S Fučik, Surjectivity of operators involving linear noninvertible part and nonlinear compact perturbation, Funk. Ekv., 17 (1974), pp. 73-83. Zbl0294.47041MR365255
23. [F-2] S Fučik, Open problems in the solvability of nonlinear equations, to appear. 
24. [F-K-N] S Fučik - M. Ku - J. Ne, Ranges of nonlinear asymptotically linear operators, J. Diff. Eq., 17 (1975), pp. 375-394. Zbl0299.47035MR372696
25. [G-H] C. Gupta - P. Hess, Existence theorems for nonlinear noncoercive operator equations and nonlinear elliptic boundary value problems, J. Diff. Eq., 22 (1976), pp. 305-313. Zbl0344.47027MR473942
26. [Ha] J. Hale, Periodic solutions of a class of hyperbolic equations containing a small parameter, Arch. Rat. Mech. Anal., 23 (1967), pp. 380-398. Zbl0152.10002MR206503
27. [He-1] P. Hess, On semicoercive nonlinear problems, Indiana Univ. Math. J., 23 (1974), pp. 645-654. Zbl0259.47051MR341214
28. [He-2] P. Hess, On a theorem by Landesman and Lazer, Indiana Univ. Math. J.23 (1974), pp. 827-830. Zbl0259.35036MR352687
29. [K-W] J. Kazdan - F. Warner, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math., 28 (1975), pp. 567-597. Zbl0325.35038MR477445
30. [L-S-U] O. Ladyzenskaja - V. Solonnikov - N. Ural'ceva, Linear and quasilinear equations of parabolic type, Translations of Math. Monographs, Vol. 23AMS (1968). Zbl0174.15403MR241822
31. [La-La] E. Landesman - A. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech., 19 (1970), pp. 609-623. Zbl0193.39203MR267269
32. [Le-Li] J. Leray - J.L. Lions, Quelques résultats de Visik sur les problèmes elliptiques nonlinéaires par les méthodes de Minty-Browder, Bull. Soc. Math. Fr., 93 (1965), pp. 97-107. Zbl0132.10502MR194733
33. [L-S] J.L. Lions - G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math., 20 (1967), pp. 493-519. Zbl0152.34601MR216344
34. [Li] W. Littman, A strong maximum principle for weakly L-subharmonic functions, J. Math. Mech., 8 (1959), pp. 761-770. Zbl0090.08201MR107746
35. [Lo] H. Lovicarova, Periodic solutions of weakly nonlinear wave equation in one dimension, Czech. Math. J., 19 (1969), pp. 324-342. Zbl0181.10901MR247249
36. [McK-R] P McKenna - J. Rauch, Strongly nonlinear perturbations of nonnegative boundary value problems with kernel, Jour. Diff. Equa., to appear. Zbl0405.34019MR491053
37. [M-1] J. Mawhin, Nonlinear perturbations of Fredholm mappings in normed spaces and applications to differential equations, Univ. de Brasilia, Trabalho de Mat., No. 61 (1974). 
38. [M-2] J. Mawhin, Periodic solutions of nonlinear telegraph equations, Proc. Int. Symp. Dyn. Syst.Gainesville, Florida (1976). Zbl0547.35077MR460914
39. [M-3] J. Mawhin, Solutions periodiques d'équations aux dérivées partielles hyperboliques nonlinéaires (to appear in a volume dedicated to TH. VOGEL). 
40. [M-4] J. Mawhin, Lecture at Oberwolfach, January 1976. 
41. [N-1] L. Nirenberg, An application of generalized degree to a class of nonlinear problems, Coll. Analyse Fonctionnelle, Liège, 1970 (Math. Vander., pp. 57-74). Zbl0317.35036MR413207
42. [N-2] L. Nirenberg, Generalized degree and nonlinear problems, Contribution to Nonlinear Functional Analysis, Zarantonello ed. (1971), Acad. Press, pp. 1-9. MR388188
43. [N-3] L. Nirenberg, Topics in Nonlinear Functional Analysis, New York Univ. Lecture Notes (1974). Zbl0286.47037MR488102
44. [O-S] J.E. Osborn - D. Sather, Alternative problems and monotonicity, J. Diff. Eq'ns., 18 (1975), pp. 393-410. Zbl0317.35024MR375023
45. [P] G. Prodi, Soluzioni periodiche delle equazioni a derivate parziali di tipo iperbolico nonlineari, Annali Mat. Pura Appl., 42 (1956), pp. 25-49. Zbl0072.10101MR89985
46. [Ra-1] P. Rabinowitz, Periodic solutions of nonlinear hyperbolic partial differential equations, Comm. Pure Appl. Math., 20 (1967), pp. 145-205. Zbl0152.10003MR206507
47. [Ra-2] P. Rabinowitz, Time periodic solutions of nonlinear wave equations, Manuscripta Math., 5 (1971), pp. 165-194. Zbl0219.35062MR326179
48. [Ra-3] P. Rabinowitz, Some minimax theorems and applications to nonlinear partial differential equations, to appear. Zbl0466.58015MR501092
49. [Ro] R.T. Rockafellar, Convex analysis, Princeton Univ. Press, 1970. Zbl0193.18401MR274683
50. [Scha] M. Schatzman, Problèmes aux limites, nonlinéaires, noncoercifs, Ann. Scuola Norm. Sup. Pisa, 27 (1973), pp. 641-686. Zbl0324.47031MR380545
51. [Sche] M. Schechter, A nonlinear elliptic boundary value problem, Ann. Scuola Norm. Sup. Pisa, 27 (1973), pp. 707-716. Zbl0302.35044MR369912
52. [Sta] G. Stampacchia, Equations elliptiques du second ordre à coefficients discontinus, Presses Univ. Montreal, (1966). Zbl0151.15501MR251373
53. [Str] W. Strauss, On weak solutions of semilinear hyperbolic equations, Anais Acad. Brasileira Ciencias, 42 (1970), pp. 645-651. Zbl0217.13104MR306715
54. [V] O. Vejvoda, Periodic solutions of nonlinear partial differential equations of evolution, Proc. Symp. Diff. Eq. and Applications, Bratislava, (1969), pp. 293-300. Zbl0183.10401MR249793
55. [W] S. Williams, A sharp sufficient condition for solution of nonlinear elliptic boundary value problem, J. Diff. Eq., 8 (1970), pp. 580-588. Zbl0209.13003MR267267

1. H. Brezis, Cordes vibrantes non linéaires
2. Thierry Gallouët, Otared Kavian, Résultats d'existence et de non-existence pour certains problèmes demi-linéaires à l'infini
3. Daniel Goeleven, Noncoercive hemivariational inequality and its applications in nonconvex unilateral mechanics
4. Věnceslava Šťastnová, Svatopluk Fučík, Note to periodic solvability of the boundary value problem for nonlinear heat equation
5. Claudio Baiocchi, Fabio Gastaldi, Franco Tomarelli, Some existence results on noncoercive variational inequalities
6. Aomar Anane, Omar Chakrone, Sur un théorème de point critique et application à un problème de non-résonance entre deux valeurs propres du $p$-laplacien
7. Jean-Michel Coron, Résolution de l’équation $Au+Bu=f$ où $A$ est linéaire et $B$ dérive d’un potentiel convexe
8. George Dinca, Panagiotis D. Panagiotopoulos, Gabriela Pop, An existence result on noncoercive hemivariational inequalities
9. Wan Se Kim, A note on the existence of solution for semilinear heat equations with polynomial growth nonlinearity
10. Andrzej Szulkin, Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems