EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A p(x)- KIRCHHOFF TYPE PROBLEM VIA VARIATIONAL TECHNIQUES

This paper discusses the existence and multiplicity of solutions for a class of p(x)-Kirchhoff type problems with Dirichlet boundary data of the following form{-(a + b integral(Omega) 1 p(x) vertical bar del u vertical bar(p(x)) dx)div(vertical bar del u vertical bar(p(x)-2)del u) = f(x, u), in Omegau = 0 on partial derivative Omega,where Omega is a smooth open subset of R-N and p is an element of C((Omega) over bar) with N p(-) inf(x is an element of Omega) p(x) = p(+) = sup(x is an element of Omega) p(x) +infinity, a, b are positive constants and f : (Omega) over bar x R - R is a continuous function. The proof is based on critical point theory and variable exponent Sobolev space theory.