Solutions of some nonlinear elliptic problems with perturbation terms of arbitrary growth

Discrete and Continuous Dynamical Systems

Volumn 10, Issue 3, 2004, Pages 617-634

  Liu, Zhaoli ^a   Su, Jiabao ^b  

^a SHANDONG UNIVERSITY   (China)

^b CAPITAL NORMAL UNIVERSITY   (China)

Author keywords

Critical group; Elliptic equation; Minimax methods; Multiplicity; Nontrivial solution; Perturbation term; Resonance

Indexed keywords

EID: 1042279410     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2004.10.617     Document Type: Article

References (21)

1. A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14(1973), 349-381.
2. P. Bartolo, V. Benci, and D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonlinear Analysis, TMA, 7(1983), 981-1012.
3. T. Bartsch and S.J. Li, Critical point theory for asymptotically quadratic functional and applications to problems with resonance, Nonlinear Analysis, TMA, 28(1997), 419-441.
4. H. Brézis and T. Kato, Remarks on the Schrödinger operator with singular complex potentials, J. Math. Pures Appl., 58(1979), 137-151.
5. G. Cerami, Un criterio di esistenza per i punti critici su varietà illimitate, Rend. Acad. Sci. Lett. Ist. Lombardo, 112(1978), 332-336.
6. C. Chambers and N. Ghoussoub, Deformation from symmetry and multiplicity of solutions in non-homogeneous problems, Discrete and Continuous Dynamical Systems, 8(2002), 267-281.
7. K.C. Chang, A variant of mountain pass lemma, Scientia Sinica, 26(1983), 1241-1255.
8. K.C. Chang, "Infinite Dimensional Morse Theory and Multiple Solution Problems", Birkhäuser, Boston, 1993.
9. 1 isolated critical points, C. R. Acad. Sci. Paris, 319 (1994), 441-446.
10. D.G. Costa and C.A. Magalhães, Variational elliptic problems which are nonquadratic at infinity, Nonlinear Analysis, TMA, 23(1994), 1401-1412.
11. D.G. de Figueiredo and Y.H. ding, Solutions of a nonlinear Schrödinger equations, Discrete and Continuous Dynamical Systems, 8(2002), 563-584.
12. D.G. de Figueiredo, P.L. Lions, and R.D. Nussbaum, A priori estimates and existence results for positive solutions of semilinear elliptic equations, J. Math. Pures Appl., 61(1982), 41-63.
13. D. Gromoll and W. Meyer, On differentiable functions with isolated critical points, Topology, 8(1969), 361-369.
14. E.A. Landesman and A.C. Lazer, Nonlinear perturbations of linear eigenvalues problems at resonance, J. Math. Mech., 19(1970), 609-623.
15. S.J. Li and Z.L. Liu, Multiplicity of solutions for some elliptic equations involving critical and supercritical sobolev exponents, preprint.
16. J.Q. Liu, The Morse index of a saddle point, Sys. Sci. Math. Sci., 2(1989), 32-39.
17. J.Q. Liu and S.P. Wu, A note on a calss of sublinear elliptic equation, preprint.
18. Z.L. Liu, Positive solutions of superlinear elliptic equations, J. Funct. Anal., 167(1999), 370-398.
19. J. Mahwin and M. Willem, "Critical Point Theory and Hamiltonian Systems", Springer, Berlin, 1989.
20. P.H. Rabinowitz, "Minimax Methods in Critical Point Theory with Applications to Differential Equations", CBMS, No. 65, Amer. Math. Soc., Providence, 1986.
21. J.B. Su, Semilinear elliptic boundary value problems with double resonance between two consecutive eigenvalues, Nonlinear Analysis, TMA. 48, 6(2002), 881-895.