... Problem for Higher-Order Abstract Differential Equations, vol. 1701 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1998.6 Advances in Difference EquationsAccording to the H¨older inequality, ... ds.3.24The right-hand side of 3.24 tends to 0 as t2→ t1as a consequence of the continuity of St in the uniform operator topology for t>0 by the compactness of St.SoI3→ 0ast2→ t1.Thus, ... permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.We study the existence and uniqueness of mild solution of a class of nonlinear...