Existence and multiplicity of solutions for a differential inclusion problem involving the p(x)-Laplacian

• Main Author: Guowei Dai
• Format: Article
• Language: English
• Published: Texas State University 2010-03-01
• Series: Electronic Journal of Differential Equations
• Subjects: p(x)-Laplacian; nonsmooth mountain pass theorem; differential inclusion
• Online Access: http://ejde.math.txstate.edu/Volumes/2010/44/abstr.html

In this article we consider the differential inclusion $$displaylines{ -hbox{div}(| abla u|^{p(x)-2} abla u)in partial F(x,u) quadhbox{in }Omega,cr u=0 quad hbox{on }partial Omega }$$ which involves the $p(x)$-Laplacian. By applying the nonsmooth Mountain Pass Theorem, we obtain at least one nontrivial solution; and by applying the symmetric Mountain Pass Theorem, we obtain k-pairs of nontrivial solutions in $W_{0}^{1,p(x)}(Omega)$.