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Nonlocal problems at critical growth in contractible domains. (English) Zbl 1333.35328
Summary: We prove the existence of a positive solution for nonlocal problems involving the fractional Laplacian and a critical growth power nonlinearity when the equation is set in a suitable contractible domain.

##### MSC:
 35R11 Fractional partial differential equations 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35B09 Positive solutions to PDEs 35B33 Critical exponents in context of PDEs 35J25 Boundary value problems for second-order elliptic equations 35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
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