Stability of solutions to differential equations of neutral type

Демиденко, Г. В.; Kotova, T. V.; Skvortsova, Maria

doi:10.1007/s10958-012-0994-x

Cited by 9 publications

(15 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…However, the estimates for exponential decay of solutions to the system (7) established in [7] are weaker than the estimates obtained in [4] if D < 1. These results were strengthened in [9] for a single delay and in [10] for several delays.…”

Section: Theorem 1 Assume That There Exist Matricesmentioning

confidence: 68%

“…4 We consider a class of systems of nonlinear differential equations of neutral type with several delays. We obtain conditions of exponential stability of the zero solution and establish estimates characterizing the exponential decay rate of solutions at infinity.…”

mentioning

confidence: 99%

“…where the matrices H and K(s) satisfy the conditions (4). Under the assumption that D < 1, exponential stability conditions and estimates for solutions to the system (5) were obtained (hereinafter, we use the spectral norm of matrices).…”

mentioning

confidence: 99%

“…Under the assumption that D < 1, exponential stability conditions and estimates for solutions to the system (5) were obtained (hereinafter, we use the spectral norm of matrices). From these estimates it follows that all solutions decay at exponential rate; moreover, the decay rate essentially depends on the matrix D. With the help of the functional (6), the exponential stability of solutions was studied in [4,5,9] for systems of neutral type differential equations of the form d dt (y(t) + Dy(t − τ )) = Ay(t) + By(t − τ ) + F (t, y(t), y(t − τ )).…”

mentioning

confidence: 99%

“…The results of [4] were extended in [7] to the case of linear neutral type systems with several delays:…”

mentioning

confidence: 99%

See 4 more Smart Citations

Estimates for Solutions of One Class of Nonlinear Neutral Type Systems with Several Delays

Демиденко

Матвеева

2016

J Math Sci

Self Cite

View full text Add to dashboard Cite

We consider a class of systems of nonlinear differential equations of neutral type with several delays. We obtain conditions of exponential stability of the zero solution and establish estimates characterizing the exponential decay rate of solutions at infinity. Bibliography: 14 titles.We consider systems of differential equations with several delays of the formwhere D, A, and B j are constant n × n-matrices, τ j > 0 are the delay parameters, τ 1 > τ k , . . . , m, and F (t, u, v 1 , . . . , v m ) is a real-valued continuous vector-valued function satisfying the Lipschitz condition with respect to u and the inequalityIn the case D = 0, systems of the form (1) are referred to as neutral type systems [1].

show abstract