Study of an impulsive second-order mixed boundary value problem with a parameter using 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 lemma and the saddle point theorem. Our goal in this study was to apply the critical point theory, neck lemma and saddle point 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 6= ti , t ∈ [0, T], −∆u 0 (ti) = Ii(u(ti)), i = 1, 2, ..., l, u 0 (0) = 0, u(T) = 0.