Mitidieri, Enzo; Vrabie, Ioan I. Differential inclusions governed by non convex perturbations of \(m\)- accretive operators. (English) Zbl 0736.34014 Differ. Integral Equ. 2, No. 4, 525-531 (1989). The authors consider the problem \(u'\in-Au(t)+Ft,u(t)\), \(u(0)=u_ 0\), where \(A:D(A)\subset X\to 2^ X\) is an \(m\)-accretive operator such that \(-A\) generates a compact semigroup (\(X\) is a separable Banach space), \(F:[0,T]\times \overline{D(A)}\to 2^ X\) is a closed-valued, lower semicontinuous map. They prove the existence of integral solutions, and if \(F(t,u)\) is also bounded by \(g_ 1(t)\| u\|+g_ 2(t)\), where \(g_ 1\), \(g_ 2\) are integrable, they show that all mild solutions are defined on all of \([0,T]\). This result is applied to nonlinear parabolic PDE. Reviewer: T.Rzezuchowski (Warszawa) Cited in 9 Documents MSC: 34A60 Ordinary differential inclusions 58D25 Equations in function spaces; evolution equations 47H20 Semigroups of nonlinear operators Keywords:compact semigroup; separable Banach space; existence of integral solutions; mild solutions; nonlinear parabolic PDE PDFBibTeX XMLCite \textit{E. Mitidieri} and \textit{I. I. Vrabie}, Differ. Integral Equ. 2, No. 4, 525--531 (1989; Zbl 0736.34014)