On doubly nonlocal fractional elliptic equations

By Giovanni Molica Bisci, Dušan D. Repovš. 2015

69 citations recorded by the source corpus.

This work is devoted to the study of the existence of solutions to nonlocal equations involving the fractional Laplacian. These equations have a variational structure and we find a nontrivial solution for them using the Mountain Pass Theorem. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. In addition, we require rather general assumptions on the local operator. As far as we know, this result is new and represent a fractional version of a classical theorem obtained working with Laplacian equations.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/10a69e445ac2766b70d21e767480aac11e9b6ffc

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In Applied Mathematics

Citations in the corpus

Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials (2016, background): “As a matter of fact, the literature on fractional operators and their applications to partially differential equations is quite large, here we would like to mention a few, see for instance [2, 11, 12, 26, 27, 35].”
A multiplicity result for a fractional Kirchhoff equation in ℝN with a general nonlinearity (2016, methodology): “More recently, in [17] has been proved the existence of infinitely many weak solutions for a Cauchy problem for a fractional Kirchhoff-type equation by using the genus theory of Krasnosel’skii; see also [6, 26, 27, 28, 29, 33] for related problems.”