Schrödinger–Kirchhoff equation involving double critical nonlinearities

Guo, Zuji; Zhang, Xinguang

doi:10.1016/j.jmaa.2018.10.079

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction and Main Results1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2019

2022

Publication Types

Select...

Article2

Other1

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Eq. (1.2) has been studied by many researchers on whole space R N and bounded domain with some boundary conditions, such as [2][3][4][5][6][7][8][9][10][11][12] and their references. Problem (1.2) contains a nonlocal coefficient (a + b Ω |∇u| 2 dx), this leads to that Eq.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Three solutions for a new Kirchhoff-type problem

Wang¹

2020

Preprint

View full text Add to dashboard Cite

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

Three solutions for a new Kirchhoff-type problem

Wang¹

2020

Preprint

View full text Add to dashboard Cite

show abstract

Existence and multiplicity of solutions for a quasilinear nonlocal problem

Cao

Wen

2019

Computers & Mathematics with Applications

View full text Add to dashboard Cite

Three solutions for a new Kirchhoff-type problem

Wang¹

2022

Differential Equations &Amp; Applications

View full text Add to dashboard Cite

This article concerns on the existence of multiple solutions for a Kirchhoff-type problem with positive and negative modulus. By applying the variational methods and algebraic analysis, we prove that there exist the only three solutions when the parameter is absolutely small than a constant, only two solutions when the parameter is absolutely equals with the constant and an unique solution when the parameter is absolutely greater than the constant. Moreover, we use the algebraic analysis to calculating the constant with the help of one of the Mountain Pass Lemma, Ekeland variational principle, and Minimax principle.

show abstract

Schrödinger–Kirchhoff equation involving double critical nonlinearities

Cited by 3 publications

References 24 publications

Three solutions for a new Kirchhoff-type problem

Three solutions for a new Kirchhoff-type problem

Existence and multiplicity of solutions for a quasilinear nonlocal problem

Three solutions for a new Kirchhoff-type problem

Contact Info

Product

Resources

About