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Infinitely many solutions for indefinite impulsive differential equations perturbed from symmetry

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Abstract

In this paper, we deal with the existence of infinitely many solutions for some superlinear indefinite impulsive differential equations under symmetry breaking situations caused by impulsive discrete perturbation. By using Bolle’s perturbation method in critical point theory, we prove a sequence of critical values tending to infinity which yield infinitely many nontrivial solutions for perturbed impulsive differential equations. Some known results in the literature are greatly improved.

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Acknowledgments

The authors would like to thank professor Y. H. Ding, C. G. Liu and W. M. Zou for valuable suggestions and detailed discussions during the Summer School on Variational methods and Infinite Dimensional Dynamical System in Central South University in Changsha.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Jinan, Jinan, 250022, Shandong, People’s Republic of China

    Liang Zhang

  2. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Xianhua Tang

  3. Department of Mathematics, China University of Mining and Technology, Xuzhou, 221116, People’s Republic of China

    Yi Chen

Authors
  1. Liang Zhang
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  2. Xianhua Tang
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  3. Yi Chen
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Corresponding author

Correspondence to Liang Zhang.

Additional information

This work is partially supported by the NNSF (No: 11571370) of China, Natural Science Foundation of Jiangsu Province of China (No: BK20140176) and Shandong Provincial Natural Science Foundation, China (No: ZR2014AP011).

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Zhang, L., Tang, X. & Chen, Y. Infinitely many solutions for indefinite impulsive differential equations perturbed from symmetry. RACSAM 111, 753–764 (2017). https://doi.org/10.1007/s13398-016-0334-y

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  • DOI: https://doi.org/10.1007/s13398-016-0334-y

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