scholarly journals Multiplicity of positive solutions for Kirchhoff type problem involving critical exponent and sign-changing weight functions

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Chang-Mu Chu
Keyword(s):  
Critical Exponent ◽  
Positive Solutions ◽  
Weight Functions ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Multiplicity Of Positive Solutions

scholarly journals Multiplicity of positive solutions for critical fractional Kirchhoff type problem with concave-convex nonlinearity

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3791-3798
Author(s):  
Chang-Mu Chu ◽  
Zhi-Peng Cai ◽  
Hong-Min Suo
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Multiplicity Of Positive Solutions

This paper is devoted to study a class of Kirchhoff type problem with critical fractional exponent and concave nonlinearity. By means of variational methods, the multiplicity of the positive solutions to this problem is obtained.

scholarly journals Twin Positive Solutions for Schrödinger-Kirchhoff-Type Problem with Singularity and Critical Exponents

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Wei Han ◽  
Yangyang Zhao
Keyword(s):  
Boundary Condition ◽  
Positive Solutions ◽  
Perturbation Methods ◽  
Dirichlet Boundary ◽  
First Eigenvalue ◽  
Type Problem ◽  
Smooth Bounded Domain ◽  
Kirchhoff Type ◽  
The First Eigenvalue ◽  
Kirchhoff Type Problem

We study in this paper the following singular Schrödinger-Kirchhoff-type problem with critical exponent -a+b∫Ω∇u2dxΔu+u=Q(x)u5+μxα-2u+f(x)(λ/uγ) in Ω,u=0 on ∂Ω, where a,b>0 are constants, Ω⊂R3 is a smooth bounded domain, 0<α<1, λ>0 is a real parameter, γ∈(0,1) is a constant, and 0<μ<aμ1 (μ1 is the first eigenvalue of -Δu=μxα-2u, under Dirichlet boundary condition). Under appropriate assumptions on Q and f, we obtain two positive solutions via the variational and perturbation methods.

A Nonhomogeneous Fractional p-Kirchhoff Type Problem Involving Critical Exponent in ℝ N

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Mingqi Xiang ◽  
Binlin Zhang ◽  
Xia Zhang
Keyword(s):  
Critical Exponent ◽  
Critical Sobolev Exponent ◽  
Type Problem ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Sobolev Exponent

AbstractThis paper concerns itself with the nonexistence and multiplicity of solutions for the following fractional Kirchhoff-type problem involving the critical Sobolev exponent:where

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