4.4 Article

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

Journal

MEDITERRANEAN JOURNAL OF MATHEMATICS
Volume 14, Issue 4, Pages -

Publisher

SPRINGER BASEL AG
DOI: 10.1007/s00009-017-0952-4

Keywords

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

Funding

  1. National Natural Science Foundation of China [11401122]
  2. Science and technology project of Qufu Normal University [xkj201607]

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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.

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