Stability of solutions for nonlocal problems

Abstract

In this paper we deal with the stability of solutions to fractional p-Laplace problems with nonlinear sources when the fractional parameter s goes to 1. We prove a general convergence result for general weak solutions which is applied to study the convergence of ground state solutions of p−fractional problems in bounded and unbounded domains as s goes to 1. Moreover, our result applies to treat the stability of p−fractional eigenvalues as s goes to 1.