Elliptic problems involving the fractional Laplacian in RN

By G. Autuori, Patrizia Pucci. 2013

268 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/390a3327eb5959691800dec580d60df71f5dae33

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

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): “We refer also to [5,41] for related problems.”
On a fractional degenerate Kirchhoff-type problem (2017, methodology): “We cite, amid the wide literature on the subject, the works [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 18, 20] where Kirchhoff-type problems (also in their stationary versions) were studied by exploiting different methods and new technical approaches.”
Ground state solutions of scalar field fractional Schrödinger equations (2015, background): “Moreover, fractional Schrödinger-type problems have been considered in some interesting papers [2,17,18].”
DENSITY PROPERTIES FOR FRACTIONAL SOBOLEV SPACES (2015, background): “Recently, in the literature a deep interest was shown for nonlocal operators, thanks to their intriguing analytical structure and in view of several applications in a wide range of contexts, such as the thin obstacle problem, optimization, finance, phase transitions, stratified materials, anomalous…”
Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations (2016, methodology): “Models governedby the fractional p-Laplacian andunboundedpotentials are investigated in [5, 22, 32].”
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].”
Superlinear Schrödinger–Kirchhoff type problems involving the fractional p–Laplacian and critical exponent (2019, methodology): “Autuori and Pucci [7] obtained a multiplicity result for fractional Laplacian problems in RN by using the mountain pass theorem and the directmethod in variationalmethods, inwhich one of two superlinear nonlinearities could be critical or even supercritical.”
Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials (2016, background): “ attention. 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]. In what follows, let us sketch the related advance involving the fractional”
Infinitely many solutions for a fractional Kirchhoff type problem via Fountain Theorem (2015, background): “we refer the reader to [3,4,9,10,39] and the references therein.”
A Nonhomogeneous Fractional p-Kirchhoff Type Problem Involving Critical Exponent in ℝN (2016, methodology): “A multiplicity result for fractional Laplacian problems inRN is obtained in [6] by using the mountain pass theorem and the direct method in variational methods, where one of two superlinear nonlinearities could be critical or even supercritical.”