Existence of solutions to a class of damped random impulsive differential equations under Dirichlet boundary value conditions

Abstract

In this paper, we study sufficient conditions for the existence of solutions to a class of damped random impulsive differential equations under Dirichlet boundary value conditions. By using variational method we first obtain the corresponding energy functional. Then the existence of critical points are obtained by using Mountain pass lemma and Minimax principle. Finally we assert the critical point of enery functional is the mild solution of damped random impulsive differential equations.

Keywords

• damped random impulsive differential equations
• mild solution
• mountain pass lemma
• minimax principle
• theoery of critical point
• energy functional