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

Autor:	Chaofeng Zhang, Rong Hu
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	Phragmén–Lindelöf method Control in coefficients Generalized Schrödinger equation Analysis QA299.6-433
Zdroj:	Boundary Value Problems, Vol 2020, Iss 1, Pp 1-14 (2020)
Druh dokumentu:	article
ISSN:	1687-2770
DOI:	10.1186/s13661-020-01385-6
Popis:	Abstract 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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/178caeb78b014b239377d276628667d0 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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