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Nonlinear semigroups and evolution governed by “generalized” dissipative operators. (English) Zbl 0818.34033
The authors consider the abstract problem $${du\over dt}\in Au(t)+ f(t)$$ for $$t\in (0, T)$$ with $$u(0)= x$$ in a real Banach space $$X$$. The aim of this paper is to study the existence and uniqueness of mild solutions of the above Cauchy problem.
Reviewer: L.Hacia (Poznań)

##### MSC:
 34G20 Nonlinear differential equations in abstract spaces 47H20 Semigroups of nonlinear operators
##### Keywords:
Banach space; existence; uniqueness; mild solutions; Cauchy problem