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Differential Equations and Dynamical Systems

, Volume 24, Issue 2, pp 135–148 | Cite as

Existence and Multiplicity of Solutions for Some Damped Dirichlet Nonlinear Impulsive Differential Equations

  • Junjun Zhou
  • Haibo ChenEmail author
  • Belal O. M. Almuaalemi
Original Research
  • 201 Downloads

Abstract

In this paper, we consider the existence and multiplicity of solutions for some damped Dirichlet nonlinear impulsive differential equations. By using the critical point theorem we give some new criteria to guarantee that the impulsive differential equation has at leat one solution or infinitely many solutions under the assumptions that the nonlinear term satisfies sublinear, superlinear or asymptotically linear. Some recent results are extended and improved.

Keywords

Dirichlet boundary value problem Impulsive effects Variational methods Critical point theory 

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2016

Authors and Affiliations

  • Junjun Zhou
    • 1
  • Haibo Chen
    • 1
    Email author
  • Belal O. M. Almuaalemi
    • 1
  1. 1.School of Mathematics and StatisticsCentral South UniversityChangshaPeople’s Republic of China

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