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

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273155, Shandong, People’s Republic of China

    Xiaoxiao Zheng

  2. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, Guangdong, People’s Republic of China

    Yadong Shang & Huafei Di

Authors
  1. Xiaoxiao Zheng
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  2. Yadong Shang
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  3. Huafei Di
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Correspondence to Xiaoxiao Zheng.

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Zheng, X., Shang, Y. & Di, H. The Time-Periodic Solutions to the Modified Zakharov Equations with a Quantum Correction. Mediterr. J. Math. 14, 152 (2017). https://doi.org/10.1007/s00009-017-0952-4

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  • DOI: https://doi.org/10.1007/s00009-017-0952-4

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