1. Three Solutions for a Neumann Partial Differential Inclusion Via Nonsmooth Morse Theory
- Author
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Dimitri Mugnai, Antonio Iannizzotto, Francesca Colasuonno, Colasuonno, Francesca, Iannizzotto, Antonio, and Mugnai, Dimitri
- Subjects
Statistics and Probability ,Pure mathematics ,Partial differential inclusion ,Mathematics::Optimization and Control ,Morse code ,01 natural sciences ,Critical point (mathematics) ,law.invention ,Mathematics - Analysis of PDEs ,law ,FOS: Mathematics ,Neumann boundary condition ,Morse theory ,0101 mathematics ,Geometry and topology ,Mathematics ,Numerical Analysis ,p-Laplacian · Partial differential inclusion · Morse theory ,Applied Mathematics ,Numerical analysis ,p-Laplacian ,010102 general mathematics ,p-Laplacian, Partial differential inclusion, Morse theory ,010101 applied mathematics ,Partial derivative ,Geometry and Topology ,Analysis ,P-Laplacian ,Analysis of PDEs (math.AP) - Abstract
We study a partial differential inclusion, driven by the p-Laplacian operator, involving a p-superlinear nonsmooth potential, and subject to Neumann boundary condi tions. 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.
- Published
- 2016
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