Spectrum of the fractional [formula omitted]-Laplacian in [formula omitted] and decay estimate for positive solutions of a Schrödinger equation

Abstract

In this paper, we prove the existence of unbounded sequence of eigenvalues for the fractional p−Laplacian with weight in RN. We also show a nonexistence result when the weight has positive integral.In addition, we show some qualitative properties of the first eigenfunction including a sharp decay estimate. Finally, we extend the decay result to the positive solutions of a Schrödinger type equation.