We seek solutions for non-cooperative elliptic systems of two Schrödinger equations which can model phenomena in Physics and Biology. General conditions are assumed under the potentials, which produce convenient spectral properties on the elliptic operator concerned; hence, the non-cooperation characterizes it as a strongly indefinite problem. Spectral theory is employed along with an abstract linking theorem developed previously by the first two authors, which is the core of our argument. Furthermore, super- and asymptotically quadratic nonlinearities are considered.

中文翻译：

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非合作椭圆系统对$$ \ mathbb {R} ^ N $$ RN中的玻色-爱因斯坦凝聚物的相互作用进行建模

我们寻求两个Schrödinger方程的非合作椭圆系统的解决方案，它们可以对物理和生物学现象进行建模。在电势下假设了一般条件，这些条件会在相关的椭圆算子上产生方便的光谱特性；因此，不合作将其描述为一个非常不确定的问题。光谱理论与前两位作者先前开发的抽象链接定理一起使用，这是我们论证的核心。此外，考虑了超级和渐近二次非线性。