Chis-Ster, Irina Existence of monotone solutions for nonlinear perturbed differential inclusions. (English) Zbl 0960.34009 Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 93, No. 2, 189-194 (1999). The author establishes a sufficient condition to assure the existence of at least one mild solution to the nonlinear differential inclusion \[ u'(t)\in Au(t)+F(u(t)), \quad u(0)=\xi\in D, \] and \(u(s)\leq u(t)\) for each \(s<t\), where \(A:D(A)\subset X\to 2^X\) is an \(m\)-dissipative operator generating a compact semigroup, \(F:D\to 2^X\) is a nonempty, closed, convex and bounded valued mapping, \(X\) is a separable Banach space, \(D\) is a locally closed set in the closure of \(D(A)\), and “\(\leq\)” is a preorder on \(D\). Reviewer: Eduardo Liz (Vigo) MSC: 34A60 Ordinary differential inclusions 34C11 Growth and boundedness of solutions to ordinary differential equations Keywords:differential inclusion; monotone solution; mild solution; admissible set-valued map PDFBibTeX XMLCite \textit{I. Chis-Ster}, Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 93, No. 2, 189--194 (1999; Zbl 0960.34009) Full Text: EuDML