Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 11, pp. 1-17.

Title: Existence of solutions for critical fractional p-Laplacian equations with 
       indefinite weights
       
Authors: Na Cui       (Lanzhou Univ., Lanzhou, Gansu 730000, China)
         Hong-Rui Sun (Lanzhou Univ., Lanzhou, Gansu 730000, China)

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.

Submitted April 1, 2020. Published March 05, 2021.
Math Subject Classifications: 35R11, 35J92, 35B33.
Key Words: Fractional p-Laplacian; critical exponent; indefinite weight.