In this paper, we develop optimal Phragmén–Lindelöf methods, based on the use of maximum modulus of optimal value of a parameter in a Schrödinger functional, by applying the Phragmén–Lindelöf theorem for a second-order boundary value problems with respect to the Schrödinger operator. Using it, it is possible to find the existence of ground state solutions of the generalized Schrödinger equation with optimal control. In spite of the fact that the equation of this type can exhibit non-uniqueness of weak solutions, we prove that the corresponding Phragmén–Lindelöf method, under suitable assumptions on control conditions of the nonlinear term, is well-posed and admits a nonempty set of solutions.

中文翻译：

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Phragmén-Lindelöf定理在具有最优控制的广义Schrödinger方程基态解存在中的应用

在本文中，我们通过对二次薛定boundary问题应用Phragmén-Lindelöf定理，根据Schrödinger泛函中参数的最优值的最大模量，开发了最佳Phragmén-Lindelöf方法操作员。使用它，可以找到具有最优控制的广义Schrödinger方程的基态解的存在。尽管该类型的方程可能表现出弱解的非唯一性，但我们证明，在对非线性项的控制条件进行适当假设的情况下，相应的Phragmén-Lindelöf方法是适当的，并且可以接受非空集解决方案。