Nonlinear Elliptic Eigenvalue Problems with Discontinuities

In this paper we study the existence of solution for two different eigenvalue problems. The first is nonlinear and the second is semilinear. Our approach is based on results from the nonsmooth critical point theory. In the first theorem we prove the existence of at least two nontrivial solutions whe...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 1999-05, Vol.233 (1), p.406-424
Main Authors: Hu, Shouchuan, Kourogenis, N.C, Papageorgiou, N.S
Format: Article
Language:English
Subjects:
compact embedding
critical point
Exact sciences and technology
Global analysis, analysis on manifolds
locally Lipschitz functions
Mathematics
maximal monotone operators
Mountain Pass Theorem
nonsmooth Palais–Smale condition
Rayleigh quotient
Sciences and techniques of general use
subdifferential
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:In this paper we study the existence of solution for two different eigenvalue problems. The first is nonlinear and the second is semilinear. Our approach is based on results from the nonsmooth critical point theory. In the first theorem we prove the existence of at least two nontrivial solutions when λ is in a half-axis. In the second theorem (based on a nonsmooth variant of the generalized mountain pass theorem), we prove the existence of at least one nontrivial solution for every λ∈R.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1999.6338