Positive solutions for Neumann boundary value problems of second-order impulsive differential equations in Banach spaces (Q417141)

Summary: The existence of positive solutions for the Neumann boundary value problem of second-order impulsive differential equations \[ -u''(t) + Mu(t) = f(t, u(t), ~t \in J, ~t \neq t_k, \] \[ -\Delta u'|_{t=t_k} = I_k(u(t_k)), ~k = 1, 2, \dots, m, ~u'(0) = u'(1) = \theta, \] in an ordered Banach space \(E\) is discussed by employing the fixed point index theory of a condensing mapping, where \(M > 0\) is a constant, \(J = [0, 1], ~f \in C(J \times K, K), ~I_k \in C(K, K), ~k = 1, 2, \dots, m\), and \(K\) is the cone of positive elements in \(E\). Moreover, an application is given to illustrate the main result.