Existence and multiplicity of solutions to boundary value problems for fourth-order impulsive differential equations

摘要

In this paper we study the existence and the multiplicity of solutions for an impulsive boundary value problem for fourth-order differential equations. The notions of classical and weak solutions are introduced. Then the existence of at least one and infinitely many nonzero solutions is proved, using the minimization, the mountain-pass, and Clarke’s theorems. MSC: 34B15, 34B37, 58E30.