In this paper we use topological degree theory and critical point theory to investigate the existence of weak solutions for the second order impulsive boundary value problem eft\{\begin{matrix} -x''(t)-ambda x(t)=f(t), teq t_j, tı (0,i), \Delta x'(t_j)=x'(t_j^+)-x'(t_j^-) = I_j(x(t_j)), j=1,2,\dots,p, x(0)=x(i) = 0, \end{matrix}\right. where λ is a positive parameter, 0 = t0 < t1 < t2 < · · · < tp < tp+1 = pi, f ∈ L2(0, pi) is a given function and I j ∈ C(R,R) for j = 1, 2, . . . , p. 1. Introduction Consider the second order impulsive boundary value problem −x′′(t) − λx(t) = f (t), t , t j, t ∈ (0, pi), ∆x′(t j) = x′(t+j ) − x′(t−j ) = I j(x(t j)), j = 1, 2, . . . , p, x(0) = x(pi) = 0, (1) where λ is a positive parameter, 0 = t0 < t1 < t2 < · · · < tp < tp+1 = pi, f ∈ L2(0, pi) is a given function and I j ∈ C(R,R) for j = 1, 2, . . . , p. Variational methods and critical point theory were used by many authors to study the existence and subsequent qualitative properties of solutions for differential equations; see for example [1-9] and the references therein.