Weak solutions for nonlinear fractional differential equations on reflexive Banach spaces.
Weak solutions of a boundary value problem for nonlinear ordinary differential equation of second order in Banach spaces
Weak solutions of differential equations in Banach spaces
In this paper we prove a theorem for the existence of pseudo-solutions to the Cauchy problem, x' = f(t,x), x(0) = x₀ in Banach spaces. The function f will be assumed Pettis-integrable, but this assumption is not sufficient for the existence of solutions. We impose a weak compactness type condition expressed in terms of measures of weak noncompactness. We show that under some additionally assumptions our solutions are, in fact, weak solutions or even strong solutions. Thus, our theorem is an essential...
Weighted Cauchy-type problem of a functional differ-integral equation.