On the Fučik spectrum for the p-Laplacian with Robin boundary condition

Nonlinear Analysis, Theory, Methods and Applications

Volumn 74, Issue 14, 2011, Pages 4671-4681

  Motreanu, Dumitru ^a   Winkert, Patrick ^b  

^a UNIVERSITÉ DE PERPIGNAN   (France)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Fucik spectrum; p Laplacian; Robin boundary conditions

Indexed keywords

ASYMPTOTIC BEHAVIORS; EIGEN-VALUE; EIGENVALUE PROBLEM; FUCIK SPECTRUM; LIPSCHITZ CONTINUOUS; P-LAPLACIAN; ROBIN BOUNDARY CONDITIONS;

EIGENVALUES AND EIGENFUNCTIONS; LAPLACE TRANSFORMS; TIME VARYING SYSTEMS;

BOUNDARY CONDITIONS;

EID: 79957914317     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2011.04.033     Document Type: Article

References (28)

1. A. Lê Eigenvalue problems for the p-Laplacian Nonlinear Anal. 64 5 2006 1057 1099
2. S. Fuk Solvability of Nonlinear Equations and Boundary Value Problems Mathematics and its Applications vol. 4 1980 D. Reidel Publishing Co. Dordrecht
3. M. Arias, and J. Campos Radial Fuik spectrum of the Laplace operator J. Math. Anal. Appl. 190 3 1995 654 666
4. N.P. Cc On nontrivial solutions of a Dirichlet problem whose jumping nonlinearity crosses a multiple eigenvalue J. Differential Equations 80 2 1989 379 404
5. E.N. Dancer Generic domain dependence for nonsmooth equations and the open set problem for jumping nonlinearities Topol. Methods Nonlinear Anal. 1 1 1993 139 150
6. C.A. Margulies, and W. Margulies An example of the Fuik spectrum Nonlinear Anal. 29 12 1997 1373 1378
7. A. Marino, A.M. Micheletti, and A. Pistoia A nonsymmetric asymptotically linear elliptic problem Topol. Methods Nonlinear Anal. 4 2 1994 289 339
8. A.M. Micheletti A remark on the resonance set for a semilinear elliptic equation Proc. Roy. Soc. Edinburgh Sect. A 124 4 1994 803 809
9. A.M. Micheletti, and A. Pistoia A note on the resonance set for a semilinear elliptic equation and an application to jumping nonlinearities Topol. Methods Nonlinear Anal. 6 1 1995 67 80
10. A. Pistoia A generic property of the resonance set of an elliptic operator with respect to the domain Proc. Roy. Soc. Edinburgh Sect. A 127 6 1997 1301 1310
11. M. Schechter The Fuk spectrum Indiana Univ. Math. J. 43 4 1994 1139 1157
12. E.N. Dancer On the Dirichlet problem for weakly non-linear elliptic partial differential equations Proc. Roy. Soc. Edinburgh Sect. A 76 4 19761977 283 300
13. D.G. de Figueiredo, and J.-P. Gossez On the first curve of the Fuik spectrum of an elliptic operator Differential Integral Equations 7 56 1994 1285 1302
14. P. Drbek Solvability and Bifurcations of Nonlinear Equations Pitman Research Notes in Mathematics Series vol. 264 1992 Longman Scientific & Technical Harlow
15. M. Cuesta, D. de Figueiredo, and J.-P. Gossez The beginning of the Fuik spectrum for the p-Laplacian J. Differential Equations 159 1 1999 212 238
16. S. Carl, and K. Perera Sign-changing and multiple solutions for the p-Laplacian Abstr. Appl. Anal. 7 12 2002 613 625
17. A.M. Micheletti, and A. Pistoia On the Fuk spectrum for the p-Laplacian Differential Integral Equations 14 7 2001 867 882
18. D. Motreanu, and M. Tanaka Sign-changing and constant-sign solutions for p-Laplacian problems with jumping nonlinearities J. Differential Equations 249 11 2010 3352 3376
19. K. Perera Resonance problems with respect to the Fuk spectrum of the p-Laplacian Electron. J. Differential Equations 2002 pages No. 36, 10 pp. (electronic)
20. K. Perera On the Fuk spectrum of the p-Laplacian NoDEA Nonlinear Differential Equations Appl. 11 2 2004 259 270
21. M. Alif Fuk spectrum for the Neumann problem with indefinite weights Partial Differential Equations Lecture Notes in Pure and Appl. Math. vol. 229 2002 Dekker New York 45 62
22. M. Arias, J. Campos, and J.-P. Gossez On the antimaximum principle and the Fuk spectrum for the Neumann p-Laplacian Differential Integral Equations 13 13 2000 217 226
23. E. Massa On a variational characterization of a part of the Fuk spectrum and a superlinear equation for the Neumann p-Laplacian in dimension one Adv. Differential Equations 9 56 2004 699 720
24. S.R. Martnez, and J.D. Rossi On the Fuk spectrum and a resonance problem for the p-Laplacian with a nonlinear boundary condition Nonlinear Anal. 59 6 2004 813 848
25. F.E. Browder Nonlinear eigenvalues problems and group invariance Functional Analysis and Related Fields, Proc. Conf. for M. Stone, Univ. of Chicago Chicago, Ill., 1968 1970 Springer New York 1 58
26. J. Neas Introduction to the Theory of Nonlinear Elliptic Equations Teubner-Texte zur Mathematik Teubner Texts in Mathematics vol. 52 1983 BSB B.G. Teubner Verlagsgesellschaft Leipzig With German, French and Russian Summaries
27. N. Ghoussoub Duality and Perturbation Methods in Critical Point Theory Cambridge Tracts in Mathematics vol. 107 1993 Cambridge University Press Cambridge
28. S.-G. Deng Positive solutions for Robin problem involving the p (x ) -Laplacian J. Math. Anal. Appl. 360 2 2009 548 560