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 $$ (-\Delta_p)^su=\lambda g(x)|u|^{p-2}u+h(x)|u|^{p_s^*-2}u \quad \text{in }\mathbb{R}^N, $$ where \(0<s<1<p<\infty\), \(N>sp\) and \(p_s^*=Np/(N-sp)\), the weight functions \(g\) may be indefinite, and \(h\) changes sign. Specifically, based on the results of asymptotic estimates for an extremal in the fractional Sobolev inequality and the discrete spectrum of fractional p-Laplacian operator, we establish an existence criterion for a nontrivial solution to this problem.
 For more information see https://ejde.math.txstate.edu/Volumes/2021/11/abstr.html