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Fractional Laplacian equations with critical Sobolev exponent. (English) Zbl 1338.35481
The paper under review extends in a fractional setting some results concerning the existence of nontrivial solutions for a class of nonlocal elliptic Dirichlet problems involving critical nonlinear terms. The basic analytic tool to establish the existence of a nontrivial solution is the linking method. The linking geometry is stated in relationship with the value of the parameter and the eigenvalues of the operator. This relation also establishes an energy criterion for the associated functional and the best constant in the fractional Sobolev embedding in order to use compactness of the Palais-Smale sequence.

MSC:
35R11 Fractional partial differential equations
35R09 Integral partial differential equations
35A15 Variational methods applied to PDEs
35S15 Boundary value problems for PDEs with pseudodifferential operators
47G20 Integro-differential operators
45G05 Singular nonlinear integral equations
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