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Existence of monotone solutions for nonlinear perturbed differential inclusions. (English) Zbl 0960.34009

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
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