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Existence of multiple solutions for some functional boundary value problems

Staněk, Svatoslav (1992)

Archivum Mathematicum

Let X be the Banach space of C 0 -functions on 0 , 1 with the sup norm and α , β X R be continuous increasing functionals, α ( 0 ) = β ( 0 ) = 0 . This paper deals with the functional differential equation (1) x ' ' ' ( t ) = Q [ x , x ' , x ' ' ( t ) ] ( t ) , where Q : X 2 × R X is locally bounded continuous operator. Some theorems about the existence of two different solutions of (1) satisfying the functional boundary conditions α ( x ) = 0 = β ( x ' ) , x ' ' ( 1 ) - x ' ' ( 0 ) = 0 are given. The method of proof makes use of Schauder linearizatin technique and the Schauder fixed point theorem. The results are modified for 2nd order functional...

Existence results for delay second order differential inclusions

Dalila Azzam-Laouir, Tahar Haddad (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, some fixed point principle is applied to prove the existence of solutions for delay second order differential inclusions with three-point boundary conditions in the context of a separable Banach space. A topological property of the solutions set is also established.

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