Three Solutions for a Neumann Partial Differential Inclusion Via Nonsmooth Morse Theory

We study a partial differential inclusion, driven by the p -Laplacian operator, involving a p -superlinear nonsmooth potential, and subject to Neumann boundary conditions. By means of nonsmooth critical point theory, we prove the existence of at least two constant sign solutions (one positive, the o...

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Bibliographic Details
Published inSet-valued and variational analysis Vol. 25; no. 2; pp. 405 - 425
Main Authors Colasuonno, Francesca, Iannizzotto, Antonio, Mugnai, Dimitri
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2017
Springer Nature B.V
Subjects
Analysis
Boundary conditions
Critical point
Laplace transforms
Mathematics
Mathematics and Statistics
Optimization
Morse theory
58E05
Partial differential inclusion
49J52
Laplacian
49K24
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Summary:We study a partial differential inclusion, driven by the p -Laplacian operator, involving a p -superlinear nonsmooth potential, and subject to Neumann boundary conditions. By means of nonsmooth critical point theory, we prove the existence of at least two constant sign solutions (one positive, the other negative). Then, by applying the nonsmooth Morse identity, we find a third non-zero solution.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-016-0387-2