Multiple solutions for a class of nonlinear boundary value problems near resonance: A variational approach

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 6, 1997, Pages 3301-3311

  Ma, To Fu ^a   Ramos, M ^b   Sanchez, L ^b  

^a STATE UNIVERSITY OF MARINGÁ   (Brazil)

^b UNIVERSITY OF LISBON   (Portugal)

Author keywords

Critical point theory; Degree theory; Positive solutions; Resonance

Indexed keywords

EID: 0042045519     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00380-X     Document Type: Article

References (18)

1. H. Amann, A note on degree theory for gradient mappings, Proc. Amer. Math. Soc. 85 (1982), 591-595.
2. A. Anane, Simplicit'e et isolation de la première valeur propre du p-Laplacian, C. R. Acad. Sci. Paris 305 (1987), 725-728.
3. L. Boccardo, F. Murat, J. P. Puel, Existence of bounded solutions for non linear elliptic unilateral problems, Ann. Mat. Pura Appl. 152(1988), 183-196.
4. 1 local minimizers, C. R. Acad. Sci. Paris 317 (1993), 465-472.
5. 1 isolated critical points, C. R. Acad. Sci. Paris 319 (1994), 441-446.
6. K.C. Chang, "Infinite dimensional Morse theory and multiple solution problems", Birkhäuser, 1993.
7. R. Chiappinelli, D. G. de Figueiredo, Bifurcation from infinity and multiple solutions for an elliptic system, Differential Integral Equations 6 (1993), 757-771.
8. R. Chiappinelli, J. Mawhin, R. Nugari, Bifurcation from infinity and multiple solutions for some Dirichlet problems with undounded nonlinearities, Nonlinear Analysis TMA 18 (1992), 1099-1112.
9. M. Chipot, "Variational Inequalities and Flow in Porous Media", Springer-Verlag, New York, 1984.
10. N. Hirano, Multiple solutions for quasilinear elliptic equations, Nonlinear Anal. T.M.A. 15 (1990), 625-638.
11. H. Höfer, A note on the topological degree at a critical point of Mountain-Pass type, Proc. Amer. Math. Soc. 90 (1984), 309-315.
12. To Fu Ma, Métodos variacionais em problemas de valores fronteira, thesis, Universidade de Lisboa, 1995.
13. J. Mawhin, K. Schmitt, Landesman-Lazer type problems at an eigenvalue of odd multiplicity, Results in Math. 14 (1988), 138-146.
14. J. Mawhin, K. Schmitt, Nonlinear eigenvalue problems with the parameter near resonance, Ann. Polon. Math. 51 (1990), 241-248.
15. M. Ramos, L. Sanchez, Variational elliptic problems involving noncoercive functionals, Proc. Roy. Soc. Edinburgh 112 A (1989), 177-185. 7
16. M. Ramos, L. Sanchez, A variational approach to multiplicity in elliptic problems near resonance, Proc. Royal Soc. Edinburgh (to appear) .
17. J.F. Rodrigues, "Obstacle problems in Mathematical Physics", North-Holland Mathematics Studies 134, 1987.
18. M. Willem, Aspects of Morse theory, Rend. Ist. Matem. Univ. Trieste 19 (1987), 155-164.