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## Annales Polonici Mathematici

2000 | 75 | 2 | 125-141
Tytuł artykułu

### Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
125-141
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-10-18
poprawiono
2000-04-17
Twórcy
• Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
autor
• Department of Mathematics, University of Ancona, Via Brecce Bianche, Ancona 60131, Italy
Bibliografia
• [1] A. Ambrosetti and P. Rabinowitz, Dual variational methods in critical theory and applications, J. Funct. Anal. 14 (1973), 349-381.
• [2] H. Brezis, Analyse fonctionnelle. Théorie et applications, Masson, 1983.
• [3] K. J. Brown and H. Budin, On the existence of positive solutions for a class of semilinear elliptic boundary value problems, SIAM J. Math. Anal. 10 (1979), 875-883.
• [4] G. Cerami, Un criterio di esistenza per i punti critici su varietà illimitate, Rend. Istit. Lombardo Sci. Lett. 112 (1978), 332-336.
• [5] K.-C. Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102-129.
• [6] F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
• [7] D. G. Costa and C. A. Magalhães, Existence results for perturbations of the p-Laplacian, Nonlinear Anal. 24 (1995), 409-418.
• [8] D. G. De Figueiredo, On the existence of multiple ordered solutions of nonlinear eigenvalue problems, ibid. 11 (1987), 481-492.
• [9] D. Goeleven, D. Motreanu and P. D. Panagiotopoulos, Multiple solutions for a class of eigenvalue problems in hemivariational inequalities, ibid. 29 (1997), 9-26.
• [10] P. Hess, On multiple positive solutions of nonlinear elliptic eigenvalue problems, Comm. Partial Differential Equations 6 (1981), 951-961.
• [11] N. C. Kurogenis and N. S. Papageorgiou, Nonsmooth critical point theory and nonlinear elliptic equations at resonance, to appear.
• [12] C. Lefter and D. Motreanu, Critical Points Methods in Nonlinear Eigenvalue Problems with Discontinuities, Internat. Ser. Numer. Math. 107, Birkhäuser, Basel, 1992.
• [13] P. Lindqvist, On the equations $div(∥Dx∥^{p-2} Dx) + λ|x|^{p-2}x = 0$, Proc. Amer. Math. Soc. 109 (1990), 157-164.
• [14] P. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Partial Differential Equations, CBMS Regional Conf. Ser. in Math. 65, Amer. Math. Soc., Providence, RI, 1986.
• [15] M. Ramos, A critical point theorem suggested by an elliptic problem with asymmetric nonlinearities, J. Math. Anal. Appl. 196 (1995), 938-946.
• [16] E. Zeidler, Nonlinear Functional Analysis and its Applications, Springer, New York, 1985.
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Bibliografia
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