Advances in Differential Equations

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

Mousomi Bhakta and Debangana Mukherjee

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1548212469

Mathematical Reviews number (MathSciNet)
MR3910033

Subjects
Primary: 35R11: Fractional partial differential equations 35J20: Variational methods for second-order elliptic equations 49J35: Minimax problems 47G20: Integro-differential operators [See also 34K30, 35R09, 35R10, 45Jxx, 45Kxx] 45G05: Singular nonlinear integral equations

Citation

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


Export citation