Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations

By Patrizia Pucci, Mingqi Xiang, Binlin Zhang. 2016

282 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/b9bcfc6df8a53d7ef4d4dd0430596d9a179bf507

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Existence of solutions for perturbed fractional p-Laplacian equations (2016, background): “in [31] also gave a positive answer to these open problems in the context of Kirchhoff problems involving the fractional p-Laplacian.”
On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent (2017, background): “The cited results turn out to be very fruitful in order to recover an elliptic PDE approach in a nonlocal framework, and they have recently been used very often, see [1, 2, 14, 17, 20, 21].”
Isotropic and anisotropic double-phase problems: old and new (2019, background): “[29,30] related to Kirchhoff problems involving nonlocal operators associated to the standard Laplace, p-Laplace or p(x)-Laplace operators.”
Critical Nonlocal Systems with Concave-Convex Powers (2016, methodology): “Let us also mention [22] where, by using variational methods and topological degree theory, Pucci, Xiang and Zhang proved multiplicity results for fractional p-Kirchhoff equations.”
A Nonhomogeneous Fractional p-Kirchhoff Type Problem Involving Critical Exponent in ℝN (2016, background): “2) is called non-degenerate if a > 0 and b ≥ 0, while it is named degenerate if a = 0 and b > 0; see [34] for some physical explanations about non-degenerate Kirchhoff problems.”
Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials (2016, background): “Here we would like to point out some interesting models involving the fractional Laplacian, such as, the fractional Schrödinger equation (see [14, 15, 22, 23, 24]), the fractional Kirchhoff equation (see [16, 32, 33, 46, 47]), the fractional porous medium equation (see [9, 45]), the fractional Yamab”