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

Pages: 753 - 764, Volume 5, Issue 4, August 2012

doi:10.3934/dcdss.2012.5.753       Abstract        References        Full Text (393.0K)       Related Articles

Antonia Chinnì - Department of Science for Engineering and Architecture (Mathematics Section), Engineering Faculty, University of Messina, Messina, 98166, Italy (email)
Roberto Livrea - Department MECMAT, Engineering Faculty, University of Reggio Calabria, Reggio Calabria, 89100, Italy (email)

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.

Keywords:  $p(x)$-Laplacian, variable exponent Sobolev space, critical points of locally Lipschitz continuous functionals, differential inclusion problem, three-critical-points theorem.
Mathematics Subject Classification:  Primary: 35J20, 35R70.

Received: April 2011;      Revised: August 2011;      Published: November 2011.

 References