Variational properties of nonlocal singular problems

We consider a general class of nonlocal problems involving the fractional Laplacian and singular nonlinearities and we deal with the variational characterization of the solutions. Even though solutions generally have not fractional Sobolev regularity, we provide a variational characterization of the solutions via a suitable action functional.

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This article discusses a general class of nonlocal problems involving the fractional Laplacian and singular nonlinearities, and addresses the variational characterization of the solutions. Despite the lack of fractional Sobolev regularity in general solutions, a variational characterization of the solutions is provided through a suitable action functional.