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Variational methods to fourth-order impulsive differential equations

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Abstract

Many dynamical systems have impulsive dynamical behaviors due to abrupt changes at certain instants during the evolution process. The mathematical description of these phenomena leads to impulsive differential equations. In this paper, we study the existence and multiplicity of solutions for fourth-order impulsive differential equations. By using the variational methods and critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one nontrivial solution, infinitely many distinct solutions under some different conditions, respectively. Some examples are given in this paper to illustrate the feasibilities of our main results.

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Authors and Affiliations

  1. Department of Mathematics, Central South University, Changsha, 410075, Hunan, People’s Republic of China

    Juntao Sun, Haibo Chen & Liu Yang

  2. Department of Mathematics, Hengyang Normal University, Hengyang, 421008, Hunan, People’s Republic of China

    Liu Yang

Authors
  1. Juntao Sun
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  2. Haibo Chen
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  3. Liu Yang
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Corresponding author

Correspondence to Juntao Sun.

Additional information

The first author was supported by the Graduate degree thesis Innovation Foundation of Central South University (CX2009B023). The second author was supported by NFSC of China (10871206).

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Sun, J., Chen, H. & Yang, L. Variational methods to fourth-order impulsive differential equations. J. Appl. Math. Comput. 35, 323–340 (2011). https://doi.org/10.1007/s12190-009-0359-x

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  • DOI: https://doi.org/10.1007/s12190-009-0359-x

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