Let be a real B-space and a ball measure of noncompactness on , . Let be continuous functions, nondecreasing, and such that 0 is the only continuous function on satisfying , , such that for any there exist and , and differentiable and satisfying , , for ,
Theorem 1: Let be a continuous function, nondecreasing, and there exist such that , . Then
Theorem 2: If , where f: [0,T] is a uniformly continuous function such that for and for any X bounded in E, and is a given Kamke function. Then . Theorem 3: Let f be a function bounded by and as in theorem 2 and is a Kamke function of C. If AT then there exists at least one solution of for , .