Nontrivial solutions for the fractional Laplacian problems without asymptotic limits near both infinity and zero

Abstract

<p style='text-indent:20px;'>In this paper we obtain the existence of nontrivial solutions for the fractional Laplacian equations with the nonlinearity may fail to have asymptotic limits at zero and at infinity. We make use of a combination of homotopy invariance of critical groups and the topological version of linking methods.