Standing waves for a class of Kirchhoff type problems in $${\mathbb {R}^3}$$ R 3 involving critical Sobolev exponents

2015 ◽  
Vol 54 (3) ◽  
pp. 3067-3106 ◽  
Author(s):  
Yi He ◽  
Gongbao Li
Keyword(s):  
Standing Waves ◽  
Kirchhoff Type ◽  
Critical Sobolev Exponents ◽  
Kirchhoff Type Problems

Concentrating Bound States for Kirchhoff Type Problems in ℝ3 Involving Critical Sobolev Exponents

2014 ◽  
Vol 14 (2) ◽  
Author(s):  
Yi He ◽  
Gongbao Li ◽  
Shuangjie Peng
Keyword(s):  
Weak Solutions ◽  
Bound States ◽  
Type Equation ◽  
Positive Parameter ◽  
Kirchhoff Type ◽  
Critical Sobolev Exponents ◽  
Kirchhoff Type Equation ◽  
Small Positive Parameter ◽  
Kirchhoff Type Problems

AbstractWe study the concentration and multiplicity of weak solutions to the Kirchhoff type equation with critical Sobolev growth,where ε is a small positive parameter and a, b > 0 are constants, f ∈ C

scholarly journals The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

2018 ◽  
Vol 26 (1) ◽  
pp. 5-41 ◽  
Author(s):  
Baoqiang Yan ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Positive Solutions ◽  
Bifurcation Theory ◽  
Sufficient Conditions ◽  
Global Bifurcation ◽  
Existence Of A Solution ◽  
Kirchhoff Type ◽  
Existence Of Positive Solutions ◽  
Global Bifurcation Theory ◽  
Necessary And Sufficient ◽  
Kirchhoff Type Problems

Abstract In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1.

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