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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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##### References:
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