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Fixed point theorems for monotone mappings in ordered Banach spaces under weak topology features

Alahmari Abdullah, Mabrouk Mohamed, Taoudi Mohamed-Aziz

Journal of Mathematics and Applications

2019

Vol. 42

5--19

We present several fixed point theorems for monotone nonlinear operators in ordered Banach spaces. The main assumptions of our results are formulated in terms of the weak topology. As an application, we study the existence of solutions to a class of first-order vectorvalued ordinary differential equations. Our conclusions generalize many well-known results.

Weak solutions for nonlinear fractional differential equations with integral boundary conditions in Banach spaces

Benchohra M., Mostefai F.

Opuscula Mathematica

2012

Vol. 32, no. 1

31-40

The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.

On bounded pseudo and weak solutions of a nonlinear differential equation in Banach spaces

Krzyśka S., Kubiaczyk I.

Demonstratio Mathematica

1999

Vol. 32, nr 2

323-330

In this paper, we prove an existence theorem for bounded pseudo and weak solution of the differential equation . XI(t) = A(t)x(t) + f(t, X(t)) where f(., X(.) ) is Pettis- integrable for each strongly absolutely continuous function X and f(t,.) is weakly-weakly sequentially continuous. We also assume some condition expressed in terms of De Blasi's measure of weak noncompactness.