### Multiplicity results for $(p,q)$ fractional elliptic equations involving critical nonlinearities

#### Abstract

In this paper, we prove the existence of infinitely many nontrivial solutions for the class of $(p,q)$ fractional elliptic equations involving concave-critical nonlinearities in bounded domains in $\mathbb{R}^N$. Further, when the nonlinearity is of convex-critical type, we establish the multiplicity of nonnegative solutions using variational methods. In particular, we show the existence of at least $cat_{\Omega}(\Omega)$ nonnegative solutions.

#### Article information

Source
Adv. Differential Equations, Volume 24, Number 3/4 (2019), 185-228.

Dates
First available in Project Euclid: 23 January 2019

Bhakta, Mousomi; Mukherjee, Debangana. Multiplicity results for $(p,q)$ fractional elliptic equations involving critical nonlinearities. Adv. Differential Equations 24 (2019), no. 3/4, 185--228. https://projecteuclid.org/euclid.ade/1548212469