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Multiplicity results for $$(p,q)$$ fractional elliptic equations involving critical nonlinearities. (English) Zbl 1442.35500
Summary: 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.

##### MSC:
 35R11 Fractional partial differential equations 35J20 Variational methods for second-order elliptic equations 49J35 Existence of solutions for minimax problems 47G20 Integro-differential operators 45G05 Singular nonlinear integral equations
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