On a class of quasilinear eigenvalue problems in RN

Mathematische Nachrichten

Volumn 278, Issue 15, 2005, Pages 1756-1765

  Kristály, Alexandra ^a   Varga, Csaba ^a  

^a BABE BOLYAI UNIVERSITY   (Romania)

Author keywords

Critical points; Multiple solutions; P Laplacian; Principle of symmetric criticality; Sublinearity

Indexed keywords

EID: 29044447631     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.200510339     Document Type: Article

References (22)

1. G. Anello, Multiple nonnegative solutions for elliptic boundary value problems involving the p-Laplacian, preprint.
2. T. Bartsch and M. Willem, Infinitely many non-radial solutions of an Euclidean scalar field equation, J. Func. Anal. 117, 447-460 (1993).
3. H. Berestycki and P. L. Lions, Nonlinear scalar field equations, Arch. Ration. Mech. Anal. 82, 313-376 (1983).
4. G. Bonanno, Some remarks on a three critical points theorem, Nonlinear Anal. 54, 651-665 (2003).
5. C. Bonanno, A critical points theorem and nonlinear differential problems, J. Global Optim. 28, 249-258 (2004).
6. G. Bonanno and P. Candito, Three solutions to a Neumann problem for elliptic equations involving the p-Laplacian, Arch. Math. Basel 80, 424-429 (2003).
7. H. Brézis, Analyse Fonctionnelle - Théorie et Applications (Masson, Paris, 1992).
8. N, Differential Integral Equations 13, 47-60 (2000).
9. A. Kristály, Infinitely many radial and non-radial solutions for a class of hemivariational inequalities, Rocky Mountain J. Math. 35, 1173-1190 (2005).
10. A. Kristály, Multiplicity results for an eigenvalue problem for hemivariational inequalities in strip-like domains, Set-Valued Anal. 13, 85-103 (2005).
11. N, Comm. Partial Differential Equations 14, 1291-1314 (1989).
12. P.-L. Lions, Symétrie et compacité dans les espaces Sobolev, J. Funct. Anal. 49, 315-334 (1982).
13. S. Marano and D. Motreanu, On a three critical point theorem for non-differentiable functions and applications to nonlinear boundary value problems, Nonlinear Anal. 48, 37-52 (2002).
14. E. Montefusco and V. Rǎdulescu, Nonlinear eigenvalue problems for quasilinear operators on unbounded domains, NoDEA Nonlinear Differential Equations Appl. 8, 481-497 (2001).
15. R. S. Palais, The principle of symmetric criticality, Comm. Math. Phys. 69, 19-30 (1979).
16. P. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics Vol. 65 (Amer. Math. Soc., Providence, RI, 1986).
17. B. Ricceri, On a three critical points theorem, Arch. Math. Basel 75, 220-226 (2000).
18. B. Ricceri, Existence of three solutions for a class of elliptic eigenvalue problems, Math. Comput. Modelling 32, 1485-1494 (2000).
19. M. Schechter, Linking Methods in Critical Point Theory (Birkhäuser, Boston, 1999).
20. M. Schechter and W. Zou, Superlinear problems, Pacific. J. Math. 214 (1), 145-160 (2004).
21. W. A. Strauss, Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55, 149-162 (1977).
22. M. Willem, Minimax Theorems (Birkhäuser, Boston, 1995).