Infinitely Many Solutions for a Class of Kirchhoff Problems Involving the p(x)-Laplacian Operator

This article is devoted to studying a class of generalized p(x)-Laplacian Kirchhoff equations in the following form: {-M(f(Omega)1/p(x) |del u|(p(x))) div ( |&del u|(p(x)-2)del u) = lambda|u|(r(x)-2)u + f(x, u) in Omega;, u = 0 on theta Omega, where Omega is a bounded domain of R-N (N >= 2) with smooth boundary theta Omega, lambda > 0, and p and r, are two continuous functions in (Omega) over bar. Using variational methods combined with some properties of the generalized Sobolev spaces, under appropriate assumptions on f and M, we obtain a number of results on the existence of solutions. In addition, we show the existence of infinitely many solutions in the case when f satisfies the evenness condition.