Existence of solutions for critical fractional p-Laplacian equations with indefinite weights

Abstract

This article concerns the critical fractional p-Laplacian equation with indefinite weights (-Δp)su = λg(x)|u|p-2 u + h(x)|u|p*s-2u in ℝN, where 0 < s < 1 < p < ∞, N > sp and p*s = Np/(N - sp), the weight functions g may be indefinite, and h changes sign. Specifically, based on the results of the asymptotic estimates for an extremal in the fractional Sobolov inequality and the discrete spectrum of fractional p-Laplacian operator, we establish an existence criterion for a nontrivial solution to this problem.