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

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 \(p_s^*=Np/(N-sp)\), weight functions \(g\) may be indefinite, \(h\) changes sign. Specifically, based on results of asymptotic estimates for an extremal in Sobolev inequality discrete spectrum operator, we establish existence criterion a nontrivial solution to this problem.
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