Multiplicity results for critical fractional equations with sign-changing weight functions

Abstract

. In this paper, we consider a time-independent fractional equation: where Ω is a smooth bounded domain, s ∈ ( 0 , 1 ) , N > 2 s 0 < q < 1, the coef fi cient functions f and g may change sign. We fi rst obtain the existence of ground state solution by the Nehari method under the combined effect of coef fi cient functions. Then we fi nd the multiplicity of positive solutions by Mountain pass theorem under some stronger conditions, and one of them is a ground state solution.