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

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

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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.

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.

Neutral equation; delay; positive components; topological principle.

DIBLÍK, J.; SVOBODA, Z.

2020

24.07.2019

AIP

9780735418547

AIP Conference Proceedings 2116

0094-243X

AIP conference proceedings

2116

1

Spojené státy americké

310005-1

310005-4

4

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