Existence of solutions of fractional p‐Laplacian systems with different critical Sobolev‐Hardy exponents

Abstract

In this paper, we investigate a fractional p-Laplacian system with different critical Sobolev-Hardy exponents. By variational methods and the Mountain-Pass lemma, positive minimizers of the related best Sobolev constants and the existence of positive solutions of the system are found.

Fractional integration by parts and Sobolev‐type inequalities for ψ$$ \psi $$‐fractional operators

“…Although, the results are investigated for functions in the spaces $$$ {L}^p $$$ and $$$ {L}^q $$$, some conditions on the parameters $$$ p,q $$$ were not clear. Other interesting works involving variational problems can be found in previous works 31–33 …”

“…Other interesting works involving variational problems can be found in previous works. [31][32][33] It is remarkable the importance and impact that fractional operators are of integration and/or differentiation has achieved in several areas. However, what can be noted is that there are some gaps even for a well-established theory.…”