The existence of multiple solutions to quasilinear elliptic equations

Bulletin of the London Mathematical Society

Volumn 37, Issue 4, 2005, Pages 592-600

  Liu, Jiaquan ^a   Liu, Shibo ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33644627554     PISSN: 00246093     EISSN: 14692120     Source Type: Journal    
DOI: 10.1112/S0024609304004023     Document Type: Article

References (17)

1. D. ARCOYA and L. ORSINA, 'Landesman-Lazer conditions and quasilinear elliptic equations', Nonlinear Anal. 28 (1997) 1623-1632.
2. T. BARTSCH and Z. L. LIU, 'On a superlinear elliptic p-Laplacian equation', J. Differential Equations 198 (2004) 149-175.
3. 1 local minimizers', C. R. Acad. Sci. Paris Sér. I Math. 317 (1993) 465-472.
4. K. C. CHANG, Infinite dimensional Morse theory and multiple solution problems, Progr. Nonlinear Differential Equations Appl. 6 (Birkhäuser, Boston, 1993).
5. 1+aα local regularity of weak solutions of degenerate elliptic equations', Nonlinear Anal. 7 (1983) 827-850.
6. G. DINCA, P. JEBELEAN and J. MAWHIN, 'Variational and topological methods for Dirichlet problems with p-Laplacian', Port. Math. (N.S.) 58 (2001) 339-378.
7. A. R. EL AMROUSS and M. MOUSSAOUI, 'Minimax principle for critical point theory in applications to quasilinear boundary value problems', J. Differential Equations 18 (2000) 1-9.
8. X. L. FAN and Z. C. LI, 'Linking and existence results for perturbations of the p-Laplacian', Nonlinear Anal. 42 (2000) 1413-1420.
9. J. P. GARCA AZORERO, I. PERAL ALONSO and J. J. MANFREDI, 'Sobolev versus Hölder local minimizers and global multiplicity for some quasilinear elliptic equations', Commun. Contemp. Math. 2 (2000) 385-404.
10. P. HESS and T. KATO, 'On some linear and nonlinear eigenvalue problems with indefinite weight functions', Comm. Partial Differential Equations 5 (1980) 999-1030.
11. S. J. LI, K. PERERA and J. B. SU, 'Computation of critical groups in elliptic boundary-value problems where the asymptotic limits may not exist', Proc. Roy. Soc. Edinburgh 131A (2001) 721-732.
12. P-2u = 0', Proc. Amer. Math. Soc. 109 (1990) 609-623.
13. J. Q. LIU and J. B. Su, 'Remarks on multiple nontrivial solutions for quasi-linear resonant problems', J. Math. Anal. Appl. 258 (2001) 209-222.
14. S. B. LIU and S. J. Li, 'Existence of solutions for asymptotically "linear" p-Laplacian equations', Bull. London Math. Soc. 36 (2004) 81-87.
15. J. MAWHIN and M. WILLEM, Critical point theory and Hamiltonian systems (Springer, Berlin, 1989).
16. J. L. VÁZQUEZ, 'A strong maximum principle for some quasilinear elliptic equations', Appl. Math. Optim. 12 (1984) 191-202.
17. Z.-Q. WANG, 'Nonlinear boundary value problems with concave and convex nonlinearities near the origin', Nonlinear Differential Equations Appl. 8 (2001) 15-33.