Existence and multiplicity of solutions for nonlocal p(x)-Laplacian equations with nonlinear Neumann boundary conditions
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China
Boundary Value Problems 2012, 2012:1 doi:10.1186/1687-2770-2012-1Published: 4 January 2012
In this article, we study the nonlocal p(x)-Laplacian problem of the following form
where Ω is a smooth bounded domain and ν is the outward normal vector on the boundary ∂Ω, and . By using the variational method and the theory of the variable exponent Sobolev space, under appropriate assumptions on f, g, a and b, we obtain some results on existence and multiplicity of solutions of the problem.
Mathematics Subject Classification (2000): 35B38; 35D05; 35J20.