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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.16601 |
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| _version_ | 1866908783394947072 |
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| author | Xu, Ruijin Su, Jiabao Tian, Rushun |
| author_facet | Xu, Ruijin Su, Jiabao Tian, Rushun |
| contents | In this paper, we study the ground state solutions of the following coupled nonlinear Schrödinger system (P) $-Δu_1-τ_1 u_1 =μ_1u_1^3+βu_1u_2^2$, $ -Δu_2-τ_2 u_2 =μ_2u_2^3+βu_1^2u_2$ in $Ω$, $u_1=u_2=0$ on $\partialΩ$, where $μ_1, μ_2>0$, $β>0$ and $Ω\subset \mathbb{R}^N (N\le3)$ is a bounded domain with smooth boundary. We are concerned with the indefinite case, i.e., $τ_1, τ_2$ are greater than or equal to the principal eigenvalue of $-Δ$ with the Dirichlet boundary datum. By delicate variational arguments, we obtain the existence of ground state solution to $(P)$, and also provide information on critical energy levels for coupling parameter $β$ in some ranges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16601 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ground state of indefinite coupled nonlinear Schrödinger systems Xu, Ruijin Su, Jiabao Tian, Rushun Analysis of PDEs 35J10, 35J47, 35J57 In this paper, we study the ground state solutions of the following coupled nonlinear Schrödinger system (P) $-Δu_1-τ_1 u_1 =μ_1u_1^3+βu_1u_2^2$, $ -Δu_2-τ_2 u_2 =μ_2u_2^3+βu_1^2u_2$ in $Ω$, $u_1=u_2=0$ on $\partialΩ$, where $μ_1, μ_2>0$, $β>0$ and $Ω\subset \mathbb{R}^N (N\le3)$ is a bounded domain with smooth boundary. We are concerned with the indefinite case, i.e., $τ_1, τ_2$ are greater than or equal to the principal eigenvalue of $-Δ$ with the Dirichlet boundary datum. By delicate variational arguments, we obtain the existence of ground state solution to $(P)$, and also provide information on critical energy levels for coupling parameter $β$ in some ranges. |
| title | Ground state of indefinite coupled nonlinear Schrödinger systems |
| topic | Analysis of PDEs 35J10, 35J47, 35J57 |
| url | https://arxiv.org/abs/2601.16601 |