Spectrum of the fractional p-Laplacian in RN and decay estimate for positive solutions of a Schrodinger equation

In this paper, we prove the existence of unbounded sequence of eigenvalues for the fractional p-Laplacian with weight in R-N. 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 Schrodinger type equation. (C) 2019 Elsevier Ltd. All rights reserved.