Existence and multiplicity of solutions for an impulsive second-order boundary value problem with Dirichlet boundary conditions via variational methods.

Abstract

In this memoiry, we have studied an impulsive second-order boundary value problem on the bounded domain [0, T], as well as the theory of critical points, the mountain pass theorem and the saddle point theorem. Our goal in this study was to apply the critical point theory, Mountain pass theorem, saddle point theorem and Symmetric Mountain Pass Theorem to verify the existence and multiplicity of solutions to the following impulsive second-order boundary value problem : ( −u 00(t) + λu(t) = f(t, u(t)), t ∈ [0, T], ∆u 0 (tj ) = Ij (u(tj )), j = 1, 2, ..., p, u(0) = u(T) = 0,