Multiple solutions for a Neumann-type differential inclusion problem involving the $p(\cdot)$-Laplacian

Antonia Chinnì; Roberto Livrea

doi:10.3934/dcdss.2012.5.753

Article Contents

2012, Volume 5, Issue 4: 753-764. Doi: 10.3934/dcdss.2012.5.753

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Multiple solutions for a Neumann-type differential inclusion problem involving the $p(\cdot)$-Laplacian

Antonia Chinnì^1, and
Roberto Livrea^2,

1.
Department of Science for Engineering and Architecture (Mathematics Section), Engineering Faculty, University of Messina, Messina, 98166
2.
Department MECMAT, Engineering Faculty, University of Reggio Calabria, Reggio Calabria, 89100

Received: March 31, 2011

Revised: July 31, 2011

Published: July 2012

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Abstract

Using a multiple critical points theorem for locally Lipschitz continuous functionals, we establish the existence of at least three distinct solutions for a Neumann-type differential inclusion problem involving the $p(\cdot)$-Laplacian.

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Mathematics Subject Classification: Primary: 35J20, 35R70.

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