Existence of strictly decreasing positive solutions of linear differential equations of neutral type

conference paper

English

The paper is concerned with a system of linear neutral differential equations y'(t) = −C(t)y(t − τ (t)) + D(t)y'(t − δ (t)) where C and D are 2 × 2 matrices with positive entries and τ, δ are continuous delays. A criterion is derived for the existence of positive strictly decreasing components of solutions for t → ∞. The proof applies a variant of the topological Wazewski principle, as developed by Rybakowski, suitable for differential equations of the delayed type. The criterion derived generalizes a similar criterion for scalar linear neutral differential equations. Solutions of the problem are taken to be continuously differentiable defined by initial functions satisfying the sewing condition.

Neutral equation; delay; positive components; topological principle.

DIBLÍK, J.; SVOBODA, Z.

24. 7. 2019

AIP

9780735418547

AIP Conference Proceedings 2116

0094-243X

AIP conference proceedings

2116

1

United States of America

310005-1

310005-4

4

https://aip.scitation.org/doi/abs/10.1063/1.5114312