A critical Kirchhoff type problem involving a nonlocal operator

By A. Fiscella, Enrico Valdinoci. 2013

471 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a00bcb85bb7500b549d24cfa0459fb02b43757aa

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Existence theorems for entire solutions of stationary Kirchhoff fractional p-Laplacian equations (2016, background): “Stationary non–degenerate Kirchhoff problems have been extensively studied in the last decades, but usually under the request that M is increasing in R0 , as in [17, 26, 29] and the reference therein.”
Existence of solutions for Kirchhoff type problem involving the non-local fractional p-Laplacian (2015, background): “In [15,34,35], in order to obtain the existence of weak solutions the authors assume that M is a nondecreasing function on [0, ∞).”
On doubly nonlocal fractional elliptic equations (2015, background): “Very recently, the nonlocal fractional counterpart of Kirchhoff-type problems has been considered (see [12] and [17, 22]).”
A Nonhomogeneous Fractional p-Kirchhoff Type Problem Involving Critical Exponent in ℝN (2016, background): “Recently in [18], Fiscella and Valdinoci first proposed a stationary Kirchhoff variational equation which models the nonlocal aspect of the tension arising from nonlocal measurements of the fractional length of the string.”
Multiple solutions for nonhomogeneous Schrödinger–Kirchhoff type equations involving the fractional p-Laplacian in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setl (2015, background): “Note that in [25,39,40], in order to consider the existence of solutions to Kirchhoff type fractional problems, the authors assumed that M is an increasing function on R0 .”
On a fractional degenerate Kirchhoff-type problem (2017, background): “This case is quite delicate and not very covered in literature, even more in the fractional setting, as explicitly pointed out in [21].”
Infinitely many solutions for a fractional Kirchhoff type problem via Fountain Theorem (2015, background): “5), see for example [23] for the Laplacian setting and [18,32] for the fractional setting.”
Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations (2016, background): “Recently, Fiscella and Valdinoci in [17] first proposed a stationary Kirchho variational model as follows:”
Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity (2014, methodology): “Indeed, Fiscella and Valdinoci propose in [20] a stationary Kirchhoff variational problem, which models, as a special significant case, the nonlocal aspect of the tension arising from nonlocal measurements of the fractional length of the string.”
Degenerate Kirchhoff-type diffusion problems involving the fractional p-Laplacian (2017, background): “In recent years, a lot of interest has grown about Kirchhoff-type problems, see for example [3, 10, 27, 35].”
Multiplicity results for the non-homogeneous fractional p-Kirchhoff equations with concave–convex nonlinearities (2015, background): “Recently, in order to consider the existence of solutions to Kirchhofftype fractional problems, the authors in [35,39,41] assumed that M is an increasing function on”