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