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Multiplicity theorems for semilinear Robin problems

Multiplicity theorems for semilinear Robin problems Abstract We consider a semilinear Robin problem driven by the Laplacian with a reaction which does not satisfy a global growth condition, only a local one. Using variational methods coupled with truncation and perturbation techniques and Morse theory, we prove two multiplicity theorems producing four and three nontrivial solutions respectively, all with precise sign. Also, we show that our results incorporate as a special case a semilinear parametric problem which has been considered primarily in the context of Dirichlet problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Calculus of Variations de Gruyter

Multiplicity theorems for semilinear Robin problems

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Publisher
de Gruyter
Copyright
Copyright © 2015 by the
ISSN
1864-8258
eISSN
1864-8266
DOI
10.1515/acv-2013-0026
Publisher site
See Article on Publisher Site

Abstract

Abstract We consider a semilinear Robin problem driven by the Laplacian with a reaction which does not satisfy a global growth condition, only a local one. Using variational methods coupled with truncation and perturbation techniques and Morse theory, we prove two multiplicity theorems producing four and three nontrivial solutions respectively, all with precise sign. Also, we show that our results incorporate as a special case a semilinear parametric problem which has been considered primarily in the context of Dirichlet problems.

Journal

Advances in Calculus of Variationsde Gruyter

Published: Jul 1, 2015

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