On fractional Laplacian problems with indefinite nonlinearity

Abstract

In this paper, we study the existence of positive solutions for the following Laplacian problem with indefinite nonlinearitywhere is a bounded domain and a(x) is a sign-changing function. For suitable conditions on a(x) and p, we prove: there exists such that problem has a positive solution for and has no positive solution for , where is the first eigenvalue of the fractional Laplacian operator.