Higher nonlocal problems with bounded potential

By Giovanni Molica Bisci, Dušan D. Repovš. 2014

64 citations recorded by the source corpus.

Abstract The aim of this paper is to study a class of nonlocal fractional Laplacian equations depending on two real parameters. More precisely, by using an appropriate analytical context on fractional Sobolev spaces due to Servadei and Valdinoci, we establish the existence of three weak solutions for nonlocal fractional problems exploiting an abstract critical point result for smooth functionals. We emphasize that the dependence of the underlying equation from one of the real parameters is not necessarily of affine type.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/801d7479e07bcf06c13b20d62e548bf9144a0d26

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In Applied Mathematics

Citations in the corpus

Multiplicity results for the non-homogeneous fractional p-Kirchhoff equations with concave–convex nonlinearities (2015, background): “The literature on fractional operators and their applications is very huge, here we just mention a few, see for example [10–20], especially [21] and [22,23] for two different fractional Laplacian involving concave–convex nonlinearities.”
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].”
Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity (2014, background): “For multiplicity results on a non–degenerate stationary Kirchhoff problem involving −LK and a nonlinearity of integral form we refer to [21] and the references therein.”
Existence of solutions for Kirchhoff type problem involving the non-local fractional p-Laplacian (2015, background): “The literature on non-local operators and their applications is very interesting and quite large, we refer the interested reader to [2,5,8,9,19,21,22,28,31,42] and the references therein.”
On a fractional degenerate Kirchhoff-type problem (2017, unknown): “The nonlocal analysis that we perform here is quite general and exploited for other goals in several recent contributions; see [26, 27, 28, 31, 32].”