On the energy functionals derived from a non-homogeneous p-Laplacian equation: Γ-convergence, local minimizers and stable transition layers

In this paper we consider a family of singularly perturbed non-homogeneous p-Laplacian problems is an element of(p) div(k(x)vertical bar del u vertical bar(P-2) del u) + k(x)g(u) = 0 in Omega subset of R-n subject to Neumann boundary conditions. We establish the Gamma-convergence of the energy functionals associate to this family of problems. As an application, we obtain the existence and profile asymptotic of a family of local minimizers in the one-dimensional case (i.e. Omega = (0, 1)). In particular, these minimizers are stable solutions which develop inner transition layer in (0,1). (C) 2019 Published by Elsevier Inc.