Impulsive integral equations in Banach spaces and applications (Q1199322)

Using the technique of measures of noncompactness it is proved that the impulsive Fredholm integral equation \[ x(t)=\int_ 0^ T H(t,s,x(s))ds+\sum_{0<t_ k<t}I_ k(x(t_ k)) \] has positive solutions. The considerations are placed in a real Banach space \(E\) ordered by a normal cone \(P\). The main tool used in the proof is a fixed point theorem for operators being strict set contractions on the cone ring \(P_{r,R}=\{x\in P\): \(r\leq\| x\|\leq R\}\). An application to a two-point boundary value problem is given.