Existence of ground state solutions for Kirchhoff-type problem with variable potential

Hu, Die; Tang, Xianhua; Zhang, Qi

doi:10.1080/00036811.2021.1947499

Cited by 4 publications

(2 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Because the Kirchhoff-type equation has a wide range of applications in many fields, such as it models several physical and biological systems, it has been widely considered in the last two decades by using variational methods, see [1][2][3][4][5][6][7][8][9][10][11] and references therein. We just introduce several results closely related to Equation (1) here.…”

Section: Introductionmentioning

confidence: 99%

On Kirchhoff-Type Equations with Hardy Potential and Berestycki–Lions Conditions

Yang

Liu

2023

Mathematics

View full text Add to dashboard Cite

The purpose of this paper is to investigate the existence and asymptotic properties of solutions to a Kirchhoff-type equation with Hardy potential and Berestycki–Lions conditions. Firstly, we show that the equation has a positive radial ground-state solution uλ by using the Pohozaev manifold. Secondly, we prove that the solution uλn, up to a subsequence, converges to a radial ground-state solution of the corresponding limiting equations as λn→0−. Finally, we provide a brief summary.

show abstract

Section: Introductionmentioning

confidence: 99%

On Kirchhoff-Type Equations with Hardy Potential and Berestycki–Lions Conditions

Yang

Liu

2023

Mathematics

View full text Add to dashboard Cite

show abstract

“…The existence and qualitative properties of solutions for (1.1) have been studied a lot, see for example, [12,26,32] and the references therein. A typical way to deal with (1.1) is to use the Mountain-Pass theorem.…”

Section: Introductionmentioning

confidence: 99%

Ground state solutions for Kirchhoff-type problems with convolution nonlinearity and Berestycki–Lions type conditions

Tang

Yuan

et al. 2021

Anal.Math.Phys.

Self Cite

View full text Add to dashboard Cite

In this paper, we discuss the following Kirchhoff-type problem with convolution nonlinearityLet f satisfies some relatively weak conditions in the absence of the usual Ambrosetti-Rabinowitz or monotonicity conditions. We get two classes of ground state solutions under the general "Berestycki-Lions conditions" on the nonlinearity f and we also give a minimax characterization of the ground state energy.

show abstract

Semiclassical Ground State Solutions for a Class of Kirchhoff-Type Problem with Convolution Nonlinearity

Tang

Zhang

2022

J Geom Anal

View full text Add to dashboard Cite

Existence of ground state solutions for Kirchhoff-type problem with variable potential

Cited by 4 publications

References 26 publications

On Kirchhoff-Type Equations with Hardy Potential and Berestycki–Lions Conditions

On Kirchhoff-Type Equations with Hardy Potential and Berestycki–Lions Conditions

Ground state solutions for Kirchhoff-type problems with convolution nonlinearity and Berestycki–Lions type conditions

Semiclassical Ground State Solutions for a Class of Kirchhoff-Type Problem with Convolution Nonlinearity

Contact Info

Product

Resources

About