On a class of second-order impulsive boundary value problem at resonance

We consider the following impulsive boundary value problem, x′′(t) = f (t,x,x′), t ∈ J \ {t1, t2, . . . , tk}, x(ti)= Ii(x(ti),x′(ti)), x′(ti)= Ji(x(ti),x′(ti)), i= 1,2, . . . ,k, x(0)= 0, x′(1) = ∑m−2 j=1 αjx′(ηj). By using the coincidence degree theory, a general theorem concerning the problem is given. Moreover, we get a concrete existence result which can be applied more conveniently than recent results. Our results extend some work concerning the usualm-point boundary value problem at resonance without impulses.