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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)Au(t)+f(t,u(t)),t(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]×DX,g:C([0,b],D)D(A) ¯ are functions with D(A)DX. Using fixed-point theorems, he proves some sufficient conditions for the existence of integral solutions, by assuming different hypotheses on f,g and A.

34G25Evolution inclusions
47H20Semigroups of nonlinear operators