On nonlocal nonlinear elliptic problem with the fractional Laplacian

Abstract

In this paper, we study a nonlocal elliptic problem with the fractional Laplacian on $R^n$. We show that the problem has infinite positive solutions in $C^\tau(R^n)\bigcap H^\alpha_{loc}(R^n)$. Moreover each of these solutions tends to some positive constant limit at infinity. We extend Lin's result to the nonlocal problem on $R^n$.