Nodal solutions of p(x)p(x)-Laplacian equations

The paper is concerned with the existence of nodal radial solutions for the p(x)p(x)-Laplacian equation {−div(|∇u|p(x)−2∇u)+a(x)|u|p(x)−2u=|u|q(x)−2uin Ω,u∈W01,p(x)(Ω).It is proved that for any given nonnegative integer kk, the problem has a pair of solutions which has exactly kk nodes when a,pa,p and qq satisfy suitable conditions.