Existence and multiplicity of solutions for a fourth-order differential system with instantaneous and non-instantaneous impulses

Abstract

The main purpose is to establish the variational structure of a fourth-order ordinary differential system with both instantaneous and non-instantaneous impulses. Then by using the mountain pass lemma and symmetric mountain pass lemma, the existence and multiplicity results of non-trivial weak solutions are obtained.

Keywords

• variational structure
• instantaneous and non-instantaneous impulse
• mountain pass theorem
• symmetric mountain pass lemma
• existence
• multiplicity
• 34a37
• 49j35