Existence of solutions for p(x)-Laplacian problem on an unbounded domain - Yongqiang, Fu (Topological Methods in Nonlinear Analysis, 2007)
In this paper we study the following p(x)-Laplacian problem: 2 -(a(x)| abla u|^p(x)-2 abla u)+b(x)|u|^p(x)-2u&=f(x,u) && xΩ, u&=0 &&on Ω, where 1< p_1p(x)p_2< n, ΩR^n is an exterior domain. Applying Mountain Pass Theorem we obtain the existence of solutions in W_0^1,p(x)(Ω) for the p(x)-Laplacian problem in the superlinear case.