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

By M. Bhakta, Debangana Mukherjee. Advances in Differential Equations, 2018

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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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

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