Ground state solutions for a non-autonomous nonlinear Schrödinger-KdV system

doi:10.1007/s11464-020-0867-4

Front. Math. China

2020, Vol. 15

Issue (5) : 851-866 https://doi.org/10.1007/s11464-020-0867-4

RESEARCH ARTICLE

Ground state solutions for a non-autonomous nonlinear Schrödinger-KdV system

Wenjing BI, Chunlei TANG(

)

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

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Abstract

We study the Schrödinger-KdV system

${− Δ u + λ 1 (x) u = u 3 + β u v, u ∈ H 1 (ℝ N), − Δ v + λ 2 (x) v = 12 v 2 + β 2 u 2, v ∈ H 1 (ℝ N),$

where $N = 1, 2, 3, λ i (x) ∈ C (ℝ N, ℝ)$ , $lim | x | → ∞ λ i (x) = λ i (∞)$ , and $λ i (x) ≤ λ i (∞)$ ,i= 1,2,a.e. $x ∈ ℝ N$ .We obtain the existence of nontrivial ground state solutions for the above system by variational methods and the Nehari manifold.

Keywords Schrödinger-KdV system variational methods Nehari manifold ground state solutions

Corresponding Author(s): Chunlei TANG

Issue Date: 19 November 2020

Cite this article:

Wenjing BI,Chunlei TANG. Ground state solutions for a non-autonomous nonlinear Schrödinger-KdV system[J]. Front. Math. China, 2020, 15(5): 851-866.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0867-4
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I5/851

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