Solitary wave of ground state type for a nonlinear Klein–Gordon equation coupled with Born–Infeld theory in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi mathvariant="normal">ℝ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>

Albuquerque, Francisco S. B.; Chen, Shangjie; Li, Lin

doi:10.14232/ejqtde.2020.1.12

Cited by 9 publications

(6 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We emphasize that unlike all previous results about system (1.1), see e.g. [1,11,14,23,25], we do not assume that the potential is the positive constant V (x) = m 2 − ω 2 . We allow the potential V be sign changing.…”

Section: Introduction and Main Resultsmentioning

confidence: 88%

Existence of high energy solutions for superlinear coupled Klein-Gordons and Born-Infeld equations

Wang,

Zhao,

Zhang

2024

ejde

View full text Add to dashboard Cite

In this article, we study the system of Klein-Gordon and Born-Infeld equations $$\displaylines{ -\Delta u +V(x)u-(2\omega+\phi)\phi u =f(x,u), \quad x\in \mathbb{R}^3,\cr \Delta \phi+\beta\Delta_4\phi=4\pi(\omega+\phi)u^2, \quad x\in \mathbb{R}^3, }$$ where $\Delta_4\phi=\hbox{div}(|\nabla\phi|^2\nabla\phi)$$, $\omega$ is a positive constant. Assuming that the primitive of $f(x,u)$ is of 2-superlinear growth in $u$ at infinity, we prove the existence of multiple solutions using the fountain theorem. Here the potential $V$ are allowed to be a sign-changing function. For more information see https://ejde.math.txstate.edu/Volumes/2024/18/abstr.html

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 88%

Existence of high energy solutions for superlinear coupled Klein-Gordons and Born-Infeld equations

Wang,

Zhao,

Zhang

2024

ejde

View full text Add to dashboard Cite

show abstract

“…Precisely, they determine the existence of a first solution by using the method of sub-and super-solutions and then prove that this solution is the minimum of a suitable functional and apply the mountain pass theorem so ensuring the existence of a second solution. For other result of fourth-order problem and variational problem, we refer the reader to [1,5,8,[10][11][12][13][14][15][16] and references therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Fourth-order elliptic problems with critical nonlinearities by a sublinear perturbation

O’Regan

2021

NAMC

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recently, for general potential V (x), Chen and Song [12] obtained the existence of multiple nontrivial solutions for (1.1) with the nonlinearity f (x, u) = λk(x)|u| q−2 u + g(x)|u| p−2 u, that is, the Klein-Gordon equation with concave and convex nonlinearities coupled with Born-Infeld theory on R 3 . Other related results about homogeneous Klein-Gordon equation with Born-Infeld theory can be found in [1,21,22,23,28].…”

mentioning

confidence: 87%

Existence of two solutions for nonhomoge- neous Klein-Gordon equation with sign-changing potential coupled with Born- Infeld theory

Wang

Zhang

Zhao

et al. 2022

Preprint

View full text Add to dashboard Cite

In this paper, we study the following nonhomogeneous Klein-Gordon equation with Born-Infeld theory −∆u + λV (x)u − K(x)(2ω + φ)φu = f (x, u) + h(x), x ∈ R 3 , ∆φ + β∆4φ = 4πK(x)(ω + φ)u 2 , x ∈ R 3 , where ω > 0 is a constant, λ > 0 is a parameter and 4φ = div(||φ| 2 φ). Under some suitable assumptions on V, K, f and h, the existence of multiple solutions is proved by using the Linking theorem and the Ekeland’s variational principle in critical point theory. Especially, the potential V is allowed to be sign-changing. Mathematics Subject Classification (2010). Primary 35B33; Secondary 35J65.

show abstract

Solitary wave of ground state type for a nonlinear Klein–Gordon equation coupled with Born–Infeld theory in ℝ2

Cited by 9 publications

References 25 publications

Existence of high energy solutions for superlinear coupled Klein-Gordons and Born-Infeld equations

Existence of high energy solutions for superlinear coupled Klein-Gordons and Born-Infeld equations

Fourth-order elliptic problems with critical nonlinearities by a sublinear perturbation

Existence of two solutions for nonhomoge- neous Klein-Gordon equation with sign-changing potential coupled with Born- Infeld theory

Contact Info

Product

Resources

About