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The Brezis-Nirenberg type problem involving the square root of the Laplacian. (English) Zbl 1248.35078
Author’s abstract: We establish existence and non-existence results to the Brezis-Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition.

MSC:
35J60 Nonlinear elliptic equations
35B09 Positive solutions to PDEs
35B33 Critical exponents in context of PDEs
35J61 Semilinear elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35R11 Fractional partial differential equations
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