Infinitely many nonradial positive solutions for two-coupled nonlinear Schrödinger equations in bbrN without symmetry
Abstract
In this paper, we consider the following two-coupled nonlinear Schrödinger equations: &−Δu+P(x)u=μu3+βuv2, in RN, &−Δv+Q(x)v=νv3+βu2v, in RN, &u, v∈ H1(RN) where N=2,3, P(x) and Q(x) are potentials, μ and ν are positive coefficients and β∈R∖{0} is the coupling parameter. By developing the intermediate reduction arguments in [del Pino-Wei-Yao, Calc. Var., 2015], we prove the existence of infinitely many nonradial positive solutions to the above system under suitable regularity and decay conditions on P(x) and Q(x), {\bf but without any symmetry assumptions on them}. The scalar version of our result also gives {\bf a positive answer} to the first part of [Question~3, del Pino-Wei-Yao, Calc. Var., 2015] and our method might be helpful in studying other problems.
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BibTeX
@misc{he2026infinitely,
title = {{Infinitely many nonradial positive solutions for two-coupled nonlinear Schrödinger equations in $\bbr^N$ without symmetry}},
author = {Rui He and Xiangqing Liu and Qingfang Wang and Yuanze Wu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07359},
eprint = {2611.07359},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07359},
}
RIS
TY - UNPB
TI - Infinitely many nonradial positive solutions for two-coupled nonlinear Schrödinger equations in bbr^N without symmetry
AU - Rui He
AU - Xiangqing Liu
AU - Qingfang Wang
AU - Yuanze Wu
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07359
UR - https://arxiv.org/abs/2611.07359
AB - In this paper, we consider the following two-coupled nonlinear Schrödinger equations: &−Δu+P(x)u=μu^3+βuv^2, in R^N, &−Δv+Q(x)v=νv^3+βu^2v, in R^N, &u, v∈ H^1(R^N) where N=2,3, P(x) and Q(x) are potentials, μ and ν are positive coefficients and β∈R∖{0} is the coupling parameter. By developing the intermediate reduction arguments in [del Pino-Wei-Yao, Calc. Var., 2015], we prove the existence of infinitely many nonradial positive solutions to the above system under suitable regularity and decay conditions on P(x) and Q(x), {\bf but without any symmetry assumptions on them}. The scalar version of our result also gives {\bf a positive answer} to the first part of [Question~3, del Pino-Wei-Yao, Calc. Var., 2015] and our method might be helpful in studying other problems.
ER -