On ground state solutions for a Kirchhoff type equation with critical growth

Lei, Chun‐Yu; Suo, Hong-Min; Chu, Changmu; Guo, Liu-Tao

doi:10.1016/j.camwa.2016.05.027

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Cited by 10 publications

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References 23 publications

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“…under some assumptions on the weight functions ( ) and ( ). The related developments of the existence of solutions for the Kirchhoff-type problems also can be found in [21][22][23][24].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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

Han

Zhao

2018

Journal of Function Spaces

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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.

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“…under some assumptions on the weight functions ( ) and ( ). The related developments of the existence of solutions for the Kirchhoff-type problems also can be found in [21][22][23][24].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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

Han

Zhao

2018

Journal of Function Spaces

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Some Results for a Class of Kirchhoff-Type Problems with Hardy–Sobolev Critical Exponent

Liao

2019

Mediterr. J. Math.

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Existence of a Positive Solution for a Class of Non-local Elliptic Problem with Critical Growth in $${\mathbb {R}}^N$$

Paes-Leme

Rodrigues

2022

Mediterr. J. Math.

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On ground state solutions for a Kirchhoff type equation with critical growth

Abstract: a b s t r a c tIn this paper, with the aid of variational method and concentration-compactness principle, a positive ground state solution is obtained for a class of Kirchhoff type equations with critical growthwhere λ > 0 is a parameter, 2 < q < 6 and k satisfies some conditions.

Cited by 10 publications

References 23 publications

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

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

Some Results for a Class of Kirchhoff-Type Problems with Hardy–Sobolev Critical Exponent

Existence of a Positive Solution for a Class of Non-local Elliptic Problem with Critical Growth in $${\mathbb {R}}^N$$

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