Positive Solutions for Neumann Boundary Value Problems of Second-Order Impulsive Differential Equations in Banach Spaces

The existence of positive solutions for Neumann boundary value problem of second-order impulsive differential equations −u″(t)+Mu(t)=f(t,u(t), t∈J, t≠tk, -Δu'|t=tk=Ik(u(tk)), k=1,2,…,m, u'(0)=u'(1)=θ, in an ordered Banach space E was discussed by employing the fixed point index theory of condensing mapping, where M>0 is a constant, J=[0,1], f∈C(J×K,K), Ik∈C(K,K), k=1,2,…,m, and K is the cone of positive elements in E. Moreover, an application is given to illustrate the main result