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

Mousomi Bhakta; Debangana Mukherjee

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arXiv · 1801.09925

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

Mousomi Bhakta·Debangana Mukherjee

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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.

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Mousomi Bhakta, Debangana Mukherjee. 2018-01-30. Multiplicity results for $(p,\, q)$ fractional elliptic equations involving critical nonlinearities. https://arxiv.org/abs/1801.09925

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