Multiple positive solutions for nonlinear critical fractional elliptic equations involving sign-changing weight functions

Abstract

In this article, we prove the existence and multiplicity of positive solutions for the following fractional elliptic equation with sign-changing weight functions: {(-Delta)(alpha)u = alpha(lambda)(x)vertical bar u vertical bar(q-2)u + b(x)vertical bar u vertical bar 2(alpha)*(-1u) in Omega, u = 0 in R-N\Omega, where 0 < alpha < 1, Omega is a bounded domain with smooth boundary in R-N with N > 2 alpha and 2(alpha)* = 2N/(N - 2 alpha) is the fractional critical Sobolev exponent. Our multiplicity results are based on studying the decomposition of the Nehari manifold and the Lusternik-Schnirelmann category.