LOCAL AND GLOBAL SOLVABILITY FOR A CLASS OF NONLOCAL DIFFERENTIAL EQUATION PERTURBED BY NONLINEARITY

Abstract

In this paper, we consider the following equation perturbed by the
nonlinearity         
γ
t t
u k A u Au f(t,u) with initial u(0) = ψ in an
arbitrary separable Hilbert space H. By using theory about completely functions
and fixed point arguments, author proves the local existence and the global
existence due to different assumptions imposed on f. The obtained results can be
applied to some concrete systems, and they are used to make the next study
such as studying on stability or regularity.