On multiple solutions of a nonlinear Dirichlet problem

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 6, 1997, Pages 3657-3662

  Castro, Alfonso ^a   Cossio, Jorge ^b   Neuberger, John M ^c  

^a UNIVERSITY OF NORTH TEXAS   (United States)

^b UNIVERSIDAD NACIONAL DE COLOMBIA   (Colombia)

^c MISSISSIPPI STATE UNIVERSITY   (United States)

Author keywords

Multiplicity of solutions; Nonlinear Dirichlet problem

Indexed keywords

EID: 0001130594     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00240-4     Document Type: Article

References (16)

1. H. AMMAN, A note on degree theory for gradient mappings, Proc. Amer. Math. Soc. 85 (1982), 591-595.
2. H. AMMAN and E. ZEHNDER, Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations, Ann. Scuola Norm. Sup. Pisa 7 (1980), 539-603.
3. A. AMBROSETTI and G. MANCINI, Sharp nonuniqueness results for some nonlinear problems, Nonlinear Anal., theory Methods 3 (1979), 635-645.
4. A. AMBROSETTI and P. RABINOWITZ, Dual variational methods in critical point theory, J. Funct. Anal. 14 (1973), 343-381.
5. L. BOCCARDO and T. GALLOUËT, Homogenization for "Castro-Lazer Equation, Nonlinear Anal. 14 (1990), 81-91.
6. N. P. CÁC, On nontrivial solutions of an asymptotically linear Dirichlet problem, J. Differential Equations 75 (1988), 103-107.
7. A. CASTRO, Métodos variacionales y análisis funcional no lineal, X Coloquio Colombiano de Matemáticas, Paipa, Colombia, 1980.
8. A. CASTRO and J. COSSIO, Multiple solutions for a nonlinear Dirichlet problem, SIAM J. Math. Anal. 25, No. 6 (1994), 1554-1561.
9. A. CASTRO and A. C. LAZER, Critical point theory and the number of solutions of a nonlinear Dirichlet problem, Ann. Mat. Pura Appl. (4) 120 (1979), 113-137.
10. K. C. CHANG, Solutions of asymptotically linear operator equations via Morse theory, Comm. Pure Appl. Math. 34 (1981), 693-712.
11. B. GIDAS, W. NI and L. NIRENBERG, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209-243..
12. H. HOFER, Variational and topological methods in partially ordered Hilbert spaces, Math. Ann. 261 (1982), 493-514.
13. A. C. LAZER and S. SOLIMINI, Nontrivial solutions of operator equations and Morse indices of critical points of min-max type, Nonlinear Anal. 12 (1988), 761-775.
14. S. LI and J. Q. LIU, Nontrivial critical points for asymptotically quadratic function, Report of International Center for Theorethical Physics IC/390, Trieste, Italy., 1986.
15. P. RABINOWITZ, Minimax methods in critical point theory with applications to differential equations, Regional conference series in Mathematics, number 65, AMS, Providence, Rhode Island, 1986.
16. J. SOTOMAYOR, Liçóes de equaçóes diferenciais ordinárias, Instituto de Matemática Pura e Aplicada, IMPA, Rio de Janeiro, 1979.