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Boundedness of Solutions of Quasi-periodic p-Laplacian Equations with Jumping Nonlinearity

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Abstract

In this article, we prove the existence of quasi-periodic solutions and the boundedness of all solutions of the p-Laplacian equation (ϕp(x′))′ + aϕp(x+) − bϕp(x−)= g(x,t) + f(t), where g(x,t) and f(t) are quasi-periodic in t with Diophantine frequency. A new method is presented to obtain the generating function to construct canonical transformation by solving a quasi-periodic homological equation.

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Authors and Affiliations

  1. School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, 266061, China

    Xin Li Zhang

  2. School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, 519082, China

    Ya Qun Peng

  3. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, China

    Da Xiong Piao

Authors
  1. Xin Li Zhang
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  2. Ya Qun Peng
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  3. Da Xiong Piao
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Corresponding author

Correspondence to Da Xiong Piao.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 11801295, 11971059, 12101623), China Postdoctoral Science Foundation (Grant No. 2020M680132) and Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020A1515110382)

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Zhang, X.L., Peng, Y.Q. & Piao, D.X. Boundedness of Solutions of Quasi-periodic p-Laplacian Equations with Jumping Nonlinearity. Acta. Math. Sin.-English Ser. 39, 176–192 (2023). https://doi.org/10.1007/s10114-022-0625-5

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  • DOI: https://doi.org/10.1007/s10114-022-0625-5

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