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Nonlinear differential equations with nonlocal conditions in Banach spaces. (English) Zbl 1095.34040
The author studies the following nonlocal initial value problem
\[ u'(t)\in Au(t)+f(t,u(t)) ,\quad t \in (0,b) , u(0)=g(u) , \]
where \(A\) is a nonlinear, \(m\)-dissipative multi-valued operator which generates a contraction semigroup \(T(t)\) in a Banach space \(X\), \(f:[0,b] \times D \to X, g: C([0,b],D) \to \overline{D(A)}\) are functions with \(D(A) \subset D \subset X\). Using fixed-point theorems, he proves some sufficient conditions for the existence of integral solutions, by assuming different hypotheses on \(f,g\) and \(A\).

MSC:
34G25 Evolution inclusions
47H20 Semigroups of nonlinear operators
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