On the existence of weak solutions of integral equations in Banach spaces

Dariusz Bugajewski

Displaying similar documents to “On the existence of weak solutions of integral equations in Banach spaces”

On the Volterra integral equation and axiomatic measures of weak noncompactness

Dariusz Bugajewski (2001)

Mathematica Bohemica

Similarity:

We prove that a set of weak solutions of the nonlinear Volterra integral equation has the Kneser property. The main condition in our result is formulated in terms of axiomatic measures of weak noncompactness.

Weak solutions of a boundary value problem for nonlinear ordinary differential equation of second order in Banach spaces

Danuta Ozdarska, Stanisław Szufla (1993)

Mathematica Slovaca

Similarity:

Kneser-type theorem for the Darboux problem in Banach spaces

Mieczysław Cichoń, Ireneusz Kubiaczyk (2001)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this paper we study the Darboux problem in some class of Banach spaces. The right-hand side of this problem is a Pettis-integrable function satisfying some conditions expressed in terms of measures of weak noncompactness. We prove that the set of all local pseudo-solutions of our problem is nonempty, compact and connected in the space of continuous functions equipped with the weak topology.