The beginning of the Fučik spectrum for the p-laplacian

Journal of Differential Equations

Volumn 159, Issue 1, 1999, Pages 212-238

  Cuesta, M ^a   De Figueiredo, D ^b   Gossez, J P ^c  

^a UNIVERSITÉ DU LITTORAL CÔTE D OPALE   (France)

^b UNIVERSITY OF CAMPINAS   (Brazil)

^c UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033589607     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1999.3645     Document Type: Article

References (30)

1. A. Anane, "Etude des Valeurs Propres et de la Résonnance Pour l'opérateur P-laplacien," Thèse, Université Libre de Bruxelles, 1987; C. R. Acad. Sci. Paris 305 (1987), 725-728.
2. A. Anane, "Etude des Valeurs Propres et de la Résonnance Pour l'opérateur P-laplacien," Thèse, Université Libre de Bruxelles, 1987; C. R. Acad. Sci. Paris 305 (1987), 725-728.
3. A. Anane and N. Tsouli, On the second eigenvalue of the p-laplacian, in "Nonlinear Partial Differential Equations" (A. Benkirane and J.-P. Gossez, Eds.), Pitman Research Notes in Mathematics, Vol. 343, pp. 1-9, Longman, Harlow/New York, 1996.
4. A. Anane and N. Tsouli, On a Nonresonnance Condition between the First and the Second Eigenvalue for the P-laplacian, preprint, 1995.
5. M. Arias and J. Campos, Radial Fučik spectrum of the laplace operator, J. Math. Anal. Appl. 190 (1995), 654-666.
6. M. Arias, J. Campos, and J.-P. Gossez, On the Antimaximum Principle and the Fučik Spectrum for the Neumann P-laplacian, to appear.
7. D. Arcoya and L. Orsina, Landesman-Lazer conditions and quasilinear elliptic equations, Nonlinear Anal. 28 (1997), 1623-1632.
8. 1 manifold, Manuscripta Math. 81 (1993), 339-359; C. R. Acad. Sci. Paris 316 (1993), 1263-1269.
9. 1 manifold, Manuscripta Math. 81 (1993), 339-359; C. R. Acad. Sci. Paris 316 (1993), 1263-1269.
10. L. Boccardo, P. Drabek, D. Giachetti, and M. Kucera, Generalization of Fredholm alternative for nonlinear differential operators, Nonlinear Anal. 10 (1986), 1083-1103.
11. H. Brezis, "Analyse Fonctionnelle, ThéOrie et Applications," Masson, Paris, 1983.
12. F. E. Browder, "Nonlinear Eigenvalue Problems and Group Invariance, Functional Analysis and Related Fields," Springer-Verlag, New York/Berlin, 1970.
13. D. Costa and M. Cuesta, Existence results for resonant perturbations of the Fučik spectrum, Topol. Methods Nonlinear Anal. 8 (1996), 295-314.
14. D. Costa and A. Oliveira, Existence of solutions for a class of semilinear problems at double resonance, Boll. Soc. Brasil. Mat. 19 (1988), 21-37.
15. M. Cuesta, "Etude de la Résonnance et du Spectre de Fučik des OpéRateurs Laplacien et p-laplacien," Thèse, Université Libre de Bruxelles, 1993.
16. M. Cuesta and J.-P. Gossez, A variational approach to nonresonance with respect to the Fučik spectrum, Nonlinear Anal. 19 (1992), 487-500.
17. N. Dancer, On the Dirichlet problem for weakly nonlinear elliptic partial differential equation, Proc. Roy. Soc. Edinburgh 76 (1977), 283-300.
18. N. Dancer, Generic domain dependance for nonsmooth equations and the open set problem for jumping nonlinearities, Topol. Methods Nonlinear Anal. 1 (1993), 139-150.
19. D. De Figueiredo, "Lectures on the Ekeland Variational Principle with Applications and Détours," TATA Institute, Springer-Verlag, New York/Berlin, 1989.
20. D. de Figueiredo and J.-P. Gossez, On the first curve of the Fučik spectrum of an elliptic operator, Differential Integral Equations 7 (1994), 1285-1302.
21. 1+α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7 (1983), 827-850.
22. P. Drabek, Solvability and bifurcations of nonlinear equations, in "Pitman Research Notes in Mathematics," Vol. 264, Longman, Harlow/New York, 1992.
23. S. Fučik, "Solvability of Nonlinear Equations and Boundary Value Problems," Reidel, Dordrecht, 1980.
24. N. Ghoussoub, "Duality and Perturbation Methods in Critical Point Theory," Cambridge Univ. Press, Cambridge, UK, 1993.
25. J.-P. Gossez and P. Omari, Nonresonnace with respect to the Fučik spectrum for periodic solutions of second order ordinary differential equations, Nonlinear Anal. 14 (1990), 1079-1104.
26. p-2 u = 0, Proc. Amer. Math. Soc. 109 (1990), 157-164; addendum, Proc. Amer. Math. Soc. 116 (1992), 583-584.
27. A. M. Micheletti, A remark on the resonance set for a semilinear elliptic equation, Proc. Roy. Soc. Edinburgh. 124 (1994), 803-809.
28. J. Nečas, "Introduction to the Theory of Nonlinear Elliptic Equations," Teubner, Leipzig, 1983.
29. P. Tolksdorf, On the Dirichlet problem for quasilinear equations in domains with conical boundary points, Comm. Partial Differential Equations 8 (1983), 773-817.
30. P-laplacien Avec Poids IndéFini," Thèse, Université Libre de Bruxelles, 1992.