The Brezis–Nirenberg type problem involving the square root of the Laplacian

By Jinggang Tan. 2011

297 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/fa0763da62d68e77b01a40f05eaffa3285ef2977

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Nonexistence results for a class of fractional elliptic boundary value problems (2012, methodology): “17) have recently been proved in [5,32] via a Pohozaev type integral identity for the extended problem.”
The Nehari manifold for fractional systems involving critical nonlinearities (2015, background): “We refer to [12, 23, 26, 27, 29, 32] for the subcritical case and to [3, 4, 11, 14, 15, 22, 24, 28] for the critical case.”
The Brezis-Nirenberg result for the fractional Laplacian (2014, methodology): “With this respect, we recall the recent paper [17], where a non-local version of the Brezis-Nirenberg result was also considered (in the case s = 1/2 and for an operator conceptually different than the one treated here).”
A critical fractional equation with concave-convex power nonlinearities (2013, background): “Some related problems involving this operator have been studied in [11,14,19,48] As in [7] the purpose of this paper is to study the existence of weak solutions for (P λ .”
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): “The literature on fractional and nonlocal operators and on their applications is very interesting and quite large, we refer the readers to [5,6,13,14,23,24,36–38,43,44,46,49,50] and the references therein.”
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.”
The Yamabe equation in a non-local setting (2013, result): “We also would like to recall the recent papers [5,21], where the authors studied a non-local version of the Brezis–Nirenberg equation for an operator conceptually different from the one treated in the present work.”
BIFURCATION AND MULTIPLICITY RESULTS FOR CRITICAL NONLOCAL FRACTIONAL LAPLACIAN PROBLEMS (2016, background): “interesting existence results for nonlocal problems driven by fractional operators in a critical setting can be found in [4, 22, 33] and references therein.”
Fractional elliptic equations with critical exponential nonlinearity (2016, background): “The critical exponent problems for the square root of Laplacian have been studied in [8, 28].”
DENSITY PROPERTIES FOR FRACTIONAL SOBOLEV SPACES (2015, background): “…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 diffusion, crystal dislocation, soft thin films, semipermeable membranes,…”
Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity (2013, background): “For related investigations on bounded domain, one can see [5, 9, 14, 18, 40] and references therein.”
Positive solutions of nonlinear problems involving the square root of the Laplacian (2009, background): “Remark 1.2. In [ 26 ] the second author J. Tan establishes the nonexistence of classical solutions to (1.1) with f(u) = up in star-shaped”
Lower semicontinuity of functionals of fractional type and applications to nonlocal equations with critical Sobolev exponent (2015, background): “Recently, a lot of interest has been devoted to this kind of problems and to their concrete applications; see, for instance the seminal papers [9, 10, 11] and [2, 3, 8, 12, 15, 16, 17, 23, 31, 40] as well as the references therein.”
The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation (2016, background): “Recently many people also studied the Brezis-Nirenberg problem for elliptic equation driven by the fractional Laplacian, this type of problem are nonlocal in nature and we may refer the readers to [6, 34, 35] and the references therein for a recent progress.”
Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian (2012, background): “We would just cite some very recent papers which analyze fractional elliptic equations involving the critical Sobolev exponent, [2, 6, 9, 16, 23, 24, 26].”