Nonlinear Schrödinger equations on periodic metric graphs

The paper is devoted to the nonlinear Schrödinger equation with periodic linear and nonlinear potentials on periodic metric graphs. Assuming that the spectrum of linear part does not contain zero, we prove the existence offinite energy ground state solution which decays exponentially fast at indinity. The proof is variational and makes use of the generalized Nehari manifold for the energy functional combined with periodic approximations. Actually, afinite energy ground state solution is obtained from periodic solutions in the infinite wave length limit.

Авторы
Pankov A. 1, 2
Издательство
American Institute of Mathematical Sciences
Номер выпуска
2
Язык
Английский
Страницы
697-714
Статус
Опубликовано
Том
38
Год
2018
Организации
  • 1 Mathematics Department, Morgan State University, Baltimore, MD 21251, United States
  • 2 RUDN University, Moscow, 117198, Russian Federation
Ключевые слова
Generalized Nehari manifold; Metric graph; Periodic approximation; Periodic nonlinear Schrödinger equation
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6870/