On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity

Abstract

We study the existence of nodal solutions to the boundary value problem −∆u = |u|p−1u in a bounded, smooth domain Ω in IR, with homogeneous Dirichlet boundary condition, when p is a large exponent. We prove that, for p large enough, there exist at least two pairs of solutions which change sign exactly once and whose nodal lines intersect the boundary of Ω.