Ground states for a class of asymptotically periodic Schrödinger–Poisson systems with critical growth

Wang, Da-Bin; Xie, Huafei; Guan, Wen

doi:10.14232/ejqtde.2017.1.97

Cited by 2 publications

(1 citation statement)

References 45 publications

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“…The appearance of the nonlocal term in the equations not only makes it important in many physical applications but also causes some difficulties and challenges from a mathematical point of view. Therefore, in the past several decades, there has been an increasing attention toward systems (1.2) or similar problems, and the existence of positive, multiple, bound state, multi-bump, as well as semiclassical state solutions has been investigated; see, for example, [4,7,9,10,13,16,21,24,29,37,38,43,[47][48][49]60]. Besides, He and Zou [23] considered multiplicity of concentrating positive solutions for a class of double parameter perturbed Schrödinger-Poisson equation with critical growth.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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

2019

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In this paper, we study the following nonlinear fractional Schrödinger-Poisson system (-) s u + V(x)u + φu = K(x)f (u), x ∈ R 3 , (-) t φ = u 2 , x ∈ R 3. (0.1) where s ∈ (3 4 , 1), t ∈ (0, 1), V, K : R 3 → R are continuous functions verifying some conditions about zero mass. By using the constraint variational method and the quantitative deformation lemma, we obtain the existence of least energy sign-changing solution to this system.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

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

2019

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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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Ground states for a class of asymptotically periodic Schrödinger–Poisson systems with critical growth

Cited by 2 publications

References 45 publications

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

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

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

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