A class of nonlinear evolution equations subjected to nonlocal initial conditions
Nonlinear evolution equation; Nonlocal initial condition; M-accretive operator; Integral solution.
This work presents a study about the existence of C^ 0-solutions for a class of nonlinear evolution equations subjected to nonlocal initial conditions, of the form
u'(t)+Au(t) \ni f(t)
f(t) \in F(t, u(t))
u(0)=g(u),
where A:D(A) \subseteq \mathcal{B} \rightarrow \mathcal{B} is an m-accretive operator acting on the infinite-dimensional Banach space \mathcal{B}, F:[0,2 \pi] \times \overline{D(A)} \rightarrow \mathcal{B} is a nonempty, convex and weakly compact valued almost strongly weakly upper semicontinuous
multi-function and g:C([0, 2 \pi]; \overline{D(A)}) \rightarrow \overline{D(A)} is a continuous function.