Multiplicity results for semilinear elliptic equations with resonance at higher eigenvalues

Nonlinear Analysis, Theory, Methods and Applications

Volumn 44, Issue 3, 2001, Pages 311-321

  Su, Jiabao ^a   Tang, Chunlei ^b  

^a Normal University   (China)

^b SW Norm University Beibei 400715   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; EIGENVALUES AND EIGENFUNCTIONS; RESONANCE; THEOREM PROVING;

MORSE THEORY; SEMILINEAR ELLIPTIC EQUATIONS;

NONLINEAR EQUATIONS;

EID: 0035314116     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(99)00265-5     Document Type: Article

References (21)

1. Bartolo P., Benci V., Fortunato D. Abstract critical point theorems and applications to nonlinear problems with "strong" resonance at infinity. Nonlinear Anal. TMA. 7:1983;981-1012.
2. Bartsch T., Li S.J. Critical point theory for asymptotically quadratic functionals and applications to problems with resonance. Nonlinear Anal. TMA. 28:1997;419-441.
3. Chang K.C. Morse theory on Banach spaces with applications. Chinese Ann. Math. 6:1983;381-399.
4. K.C. Chang, Infinite dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston, 1993.
5. 1 isolated critical points C. R. Acad. Sci. Paris, Sér. I. 319:1994;441-446.
6. Chang K.C., Li S.J., Liu J.Q. Remarks on multiple solutions for asymptotically linear elliptic boundary value problems. Topol. Methods Nonlinear Anal. 3:1994;179-187.
7. Costa D.G., Silva E.A. On a class of resonant problems at higher eigenvalues. Differential Integral Equations. 8:1995;663-671.
8. Gromoll D., Meyer W. On differential functions with isolated point. Topology. 8:1969;361-369.
9. Landesman E.M., Lazer A.C. Nonlinear perturbations of linear eigenvalues problem at resonance. J. Math. Mech. 19:1970;609-623.
10. Li S.J., Liu J.Q. Nontrivial critical point for asymptotically quadratic functions. J. Math. Anal. Appl. 165:1992;333-345.
11. S.J. Li, J.Q. Liu, Computations of critical groups at degenerate critical point and application to nonlinear differential equations with resonance, Houston J. Math., to appear.
12. Li S.J., Su J.B. Existence of multiple solutions of two-point boundary value problem at resonance. Topol. Methods Nonlinear Anal. 10:1997;123-135.
13. Landesman E., Robinson S., Rumbos A. Multiple solutions of semilinear elliptic problems at resonance. Nonlinear Anal. TMA. 24:1995;1049-1059.
14. Li S.J., Willew M. Applications of local linking to critical point theory. J. Math. Anal. Appl. 189:1995;6-32.
15. Mizoguchi N. Asymptotically linear elliptic equation without nonresonance conditions. Differential Equations. 113:1994;150-165.
16. J. Mawhin, M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, Berlin, 1989.
17. P. Rabinowitz, Minimax Methods in Critical Point Theory with Application to Differential Equations, CBMS, Vol. 65, American Mathematical Society, Providence, RI, 1986.
18. Schechter M. Elliptic resonance problems with inequal limits at infinity. Math. Ann. 300:1994;629-642.
19. Schechter M. Bounded Resonance problem for semilinear elliptic equations. Nonlinear Anal. TMA. 24:1995;1471-1482.
20. Su J.B. Semilinear elliptic resonant problems at higher eigenvalue with unbounded nonlinear terms. Acta. Math. Sinica, New Series. 14(3):1998;411-418.
21. M. Struwe, Variational Methods, Springer, Berlin, 1990.