The aim of this paper is to study the non-cooperative elliptic Schrödinger systems arising in Bose–Einstein condensation phenomena and some nonlinear optical materials. The more delicate case of systems of negative potentials is considered. We prove the existence and multiplicity of nontrivial solutions for the above system in space dimensions \(N\ge 3\). Our proofs are based on symmetric mountain pass method, the monotone iterative method, as well as suitable Schrödinger test-function arguments.

中文翻译：

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求解具有控制约束的椭圆薛定谔系统

本文的目的是研究在玻色-爱因斯坦凝聚现象和一些非线性光学材料中产生的非合作椭圆薛定谔系统。考虑了负电位系统的更微妙的情况。我们证明了上述系统在空间维度\(N\ge 3\)上非平凡解的存在性和多重性。我们的证明基于对称山口方法、单调迭代方法以及合适的薛定谔测试函数参数。