A Cauchy Problem on Time Scales with Applications

Abstract

We obtain the existence of continuous solutions for a nonlocal Cauchy problem on time scales in Banach spaces, considering non-absolutely convergent delta- integrals. As this kind of problems contains the classical cases of differential and difference equations and not only these ones, our main theorem offers a very general existence result. We then deduce, by an embedding procedure, a result for impulsive differential equations under a new kind of assumptions on the jump functions. Mathematics Subject Classication 2000: 28B05, 26A39, 39A12, 34K45.