Existence of least-energy sign-changing solutions for Schrödinger-Poisson system with critical growth

Wang, Da-Bin; Zhang, Hua-Bo; Guan, Wen

doi:10.1016/j.jmaa.2019.07.052

Cited by 47 publications

(23 citation statements)

References 37 publications

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“…Latter, under some more weak assumptions on f , Chen and Tang [11] improve and generalize some results obtained in [46]. For the other work on a sign-changing solution of system (1.5) or similar problems, we refer the reader to [5,20,21,27,30,56,68] and the references therein. It is noticed that there are some interesting results, for example [10,13,53,61], considered sign-changing solutions for other nonlocal problems.…”

Section: Introductionsupporting

confidence: 53%

Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R 3 $\mathbb{R}^{3}$

Wang

Hao

2019

Bound Value Probl

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In this paper, we study the following Kirchhoff-Schrödinger-Poisson systems:-(a + b R 3 |∇u| 2 dx) u + V(x)u + φu = f (u), x ∈ R 3 ,-φ = u 2 , x ∈ R 3 , where a, b are positive constants, V ∈ C(R 3 , R +). By using constraint variational method and the quantitative deformation lemma, we obtain a least-energy sign-changing (or nodal) solution u b to this problem, and study the energy property of u b. Moreover, we investigate the asymptotic behavior of u b as the parameter b 0.

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Section: Introductionsupporting

confidence: 53%

Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R 3 $\mathbb{R}^{3}$

Wang

Hao

2019

Bound Value Probl

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“…This type of equation has very interesting physical background which is a model to describe the nonlinear Klein–Gordon field interacting with the electromagnetic field. Along with the development of variational methods, many mathematicians used these methods to investigate the existence and multiplicity of solutions for differential equations equations(see [1, 2, 5–24, 26, 28]). In 2001, V. Benci and D. Fortunato [5] considered the following systems

\begin{matrix} true \\ right \{\begin{matrix} left - normalΔ u + true[m^{2} - {false(ω + ϕ false)}^{2} true] u = {false| u false|}^{q - 2} u & left in R^{3}, \\ left - normalΔ ϕ + ϕ u^{2} = - ω u^{2} & left in R^{3} . \end{matrix} \end{matrix}

By using the variational methods, they obtained infinitely many solitary wave solutions when

| m | > | ω |

and

4 < q < 6

.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Multiple solutions for superlinear Klein–Gordon–Maxwell equations†

Lin

2020

Mathematische Nachrichten

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In this paper, we consider the following Klein–Gordon–Maxwell equations trueright84.0pt{−Δu+V(x)u−(2ω+ϕ)ϕu=f(x,u)+h(x)indouble-struckR3,−Δϕ+ϕu2=−ωu2indouble-struckR3,where ω>0 is a constant, u, ϕ:double-struckR3→R, V:double-struckR3→R is a potential function. By assuming the coercive condition on V and some new superlinear conditions on f, we obtain two nontrivial solutions when h is nonzero and infinitely many solutions when f is odd in u and h≡0 for above equations.

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“…By using the concentration-compactness principle in fractional Sobolev spaces, they showed the existence of m pairs of solutions for any m ∈ ℕ, and by applying Krasnoselskii's genus theory, they also got the existence of infinitely many solutions under some suitable conditions for the parameter. For more information on this direction, one can refer to [17][18][19][20][21][22][23][24] and the references therein.…”

Section: Introductionmentioning

confidence: 99%