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The Time-Periodic Solutions to the Modified Zakharov Equations with a Quantum Correction

  • Xiaoxiao Zheng
  • Yadong Shang
  • Huafei Di
Article

Abstract

This paper investigates the existence and uniqueness of time-periodic solutions of the periodic initial value problem for the modified Zakharov equations with a quantum correction. By combining a priori estimates with the Galerkin method and Leray–Schauder fixed point theorem, we prove that there exist a unique strong time-periodic solution and a unique classical time-periodic solution under some conditions on the forcing terms f and g.

Keywords

modified Zakharov equations quantum correction time-periodic solution a priori estimate Galerkin method Leray–Schauder fixed point theorem 

Mathematics Subject Classification

35B10 35G25 35Q55 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesQufu Normal UniversityQufuPeople’s Republic of China
  2. 2.School of Mathematics and Information ScienceGuangzhou UniversityGuangzhouPeople’s Republic of China

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