Positive Solutions for a nth-Order Impulsive Differential Equation with Integral Boundary Conditions

In this paper we study the existence of positive solutions for the following nthorder impulsive boundary value problem { u((n)) (t) + f (t, u(t)) = 0, t is an element of[0, 1], t not equal t(k), -Delta u((n-1)) vertical bar(t=tk) = I-k (u(t(k))), k = 1, 2,..., m, u(0) = integral(1)(0) u(t)d alpha(t), u(1) = integral(1)(0) u(t)d beta(t), u'(0) = . . . = u((n-3)) (0) = u((n-2)) (0) = 0. Here f is an element of C ([0, 1] x R+, R+), I-k is an element of C(R+, R+)(R+ := [0, infinity)) and integral(1)(0) u(t)d alpha(t), integral(1)(0) u(t)d beta(t) are Riemann-Stieltjes integrals (i.e., alpha(t) and beta(t) have bounded variation). We use the Krasnoselskii-Zabreiko fixed point theorem to establish our main results. Furthermore, our nonlinear term f is allowed to grow superlinearly and sublinearly.