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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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Full Text: Euclid