Weak almost periodic and optimal mild solutions of fractional evolution equations.
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...
Weakly almost periodic solutions of linear equations in Banach spaces
Weighted Cauchy-type problem of a functional differ-integral equation.
Well-posedness of abstract Cauchy problems.
Well-posedness of the boundary value problem for parabolic equations in difference analogues of spaces of smooth functions.
Well-posedness of the difference schemes of the high order of accuracy for elliptic equations.
When unit groups of continuous inverse algebras are regular Lie groups
It is a basic fact in infinite-dimensional Lie theory that the unit group of a continuous inverse algebra A is a Lie group. We describe criteria ensuring that the Lie group is regular in Milnor’s sense. Notably, is regular if A is Mackey-complete and locally m-convex.