MULTIPLE SOLUTIONS FOR NONLINEAR DISCONTINUOUS STRONGLY RESONANT ELLIPTIC PROBLEMS

We consider quasilinear strongly resonant problems with discontinuous right‐hand side. To develop an existence theory we pass to a multivalued problem by, roughly speaking, filling in the gaps at the discontinuity points. We prove the existence of at least three nontrivial solutions. Our approach us...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2000-01, Vol.2000 (2), p.119-135
Main Authors: Kourogenis, Nikolaos C., Papageorgiou, Nikolaos S.
Format: Article
Language:English
Subjects:
35J20
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Summary:We consider quasilinear strongly resonant problems with discontinuous right‐hand side. To develop an existence theory we pass to a multivalued problem by, roughly speaking, filling in the gaps at the discontinuity points. We prove the existence of at least three nontrivial solutions. Our approach uses the nonsmooth critical point theory for locally Lipschitz functionals due to Chang (1981) and a generalized version of the Ekeland variational principle. At the end of the paper we show that the nonsmooth Palais‐Smale (PS)‐condition implies the coercivity of the functional, extending this way a well‐known result of the “smooth” case.
ISSN:1085-3375
1687-0409
DOI:10.1155/S1085337500000269