Article

Journal of Applied Mathematics and Computing

, Volume 35, Issue 1, pp 323-340

Variational methods to fourth-order impulsive differential equations

  • Juntao SunAffiliated withDepartment of Mathematics, Central South University Email author 
  • , Haibo ChenAffiliated withDepartment of Mathematics, Central South University
  • , Liu YangAffiliated withDepartment of Mathematics, Central South UniversityDepartment of Mathematics, Hengyang Normal University

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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.

Impulsive differential equations Boundary value problems Critical points Variational methods

Mathematics Subject Classification (2000)

34B15 34B37