An application of Phragmén–Lindelöf theorem to the existence of ground state solutions for the generalized Schrödinger equation with optimal control

In this paper, we develop optimal Phragmen–Lindelof methods, based on the use of maximum modulus of optimal value of a parameter in a Schrodinger functional, by applying the Phragmen–Lindelof theorem for a second-order boundary value problems with respect to the Schrodinger operator. Using it, it is possible to find the existence of ground state solutions of the generalized Schrodinger 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 Phragmen–Lindelof method, under suitable assumptions on control conditions of the nonlinear term, is well-posed and admits a nonempty set of solutions.