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On a boundary value problem on the half-line for nonlinear two-dimensional delay differential systems

100%

Philos C.

Annales Polonici Mathematici

2007

tom 92

nr 2

133-153

This article is concerned with a boundary value problem on the half-line for nonlinear two-dimensional delay differential systems. By the use of the Schauder-Tikhonov theorem, a result on the existence of solutions is obtained. Also, via the Banach contraction principle, another result concerning the existence and uniqueness of solutions is established. Moreover, these results are applied to the special case of ordinary differential systems and to a certain class of delay differential systems. Furthermore, applications to differential systems of Emden-Fowler type and to linear differential systems are presented, and two specific examples are given.

Multiple positive solutions for a second order delay boundary value problem on the half-line

51%

Mavridis K., Philos C., Tsamatos P.

Annales Polonici Mathematici

2006

tom 88

nr 2

173-191

Second order nonlinear delay differential equations are considered, and Krasnosel'skiĭ's fixed point theorem is used to establish a result on the existence of positive solutions of a boundary value problem on the half-line. This result can be used to guarantee the existence of multiple positive solutions. A specification of the result obtained to the case of second order nonlinear ordinary differential equations as well as to a particular case of second order nonlinear delay differential equations is also presented. The applicability of the main result is demonstrated by an example.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Philos C.

1 Mavridis K.

1 Tsamatos P.

1 2007

1 2006

Wyniki wyszukiwania

On a boundary value problem on the half-line for nonlinear two-dimensional delay differential systems

Multiple positive solutions for a second order delay boundary value problem on the half-line