Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth

By Jun Wang, Lixin Tian, Junxiang Xu, Fubao Zhang. 2012

370 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/3f8ba7d38fe4db6667f23a6449b578a5d4125dac

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Existence and concentration of positive ground states for a Kirchhoff equation involving critical Sobolev exponent (2014, background): “[42], Zhao and Zhao [47], and we here sketch the proof for the completeness of the presentation.”
On ground states for the Kirchhoff-type problem with a general critical nonlinearity (2015, background): “For this subject we refer, for example, to [18,35,27,15].”
Positive solutions of Kirchhoff type elliptic equations involving a critical Sobolev exponent (2014, neutral): “For (K1) with Ω = R , see [3,22,35].”
Existence and multiplicity of solutions for Kirchhoff type problem with critical exponent (2013, neutral): “[13].”
Existence of positive solutions to Kirchhoff type problems with zero mass (2014, neutral): “There are few papers considering Kirchhoff type problems on RN except [8,9,12,17,25,26].”
Existence and concentration of positive solutions for semilinear Schrödinger–Poisson systems in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin} (2012, neutral): “4(see [32]), we know that there exist C, δ > 0 (independent of ε) such that hε(x) ≤ Ce−δ|x |, where hε = uε(x + yε) and uε(yε) = maxy∈RN uε.”
Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities (2014, background): “In [35], He, Li and Peng studied (Pε) in a similar situation to [62], namely, N = 3, M(t) = a + bt and f (s) = g(s)+ |s|4s where g(s) = o(s3) as s → 0 and g(s)/s3 is strictly increasing.”
Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in $R^3$ (2013, methodology): “In [16] and [33], V (x) satisfies (V5), then the method used in [21][18][24][35] can not work.”