Advances in Differential Equations

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

Mousomi Bhakta and Debangana Mukherjee

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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

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

First available in Project Euclid: 23 January 2019

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Mathematical Reviews number (MathSciNet)

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


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.

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