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Integro-differential equations and delay integral inequalities

In this paper, we consider certain non-linear scalar Volterra integro-differential equations and Volterra integro-differential systems of first order. We investigate the boundedness, stability, uni...

New qualitative criteria for solutions of Volterra integro-differential equations

New stability and boundedness results to Volterra integro-differential equations with delay

https://www.tandfonline.com/doi/pdf/10.1080/16583655.2018.1451117

On behaviours of functional Volterra integro-differential equations with multiple time lags

Asymptotic stability and boundedness criteria for nonlinear retarded Volterra integro-differential equations

where $A$ is a constant $n¥times n$ matrix, $C(t, s)$ is an $n¥times n$ matrix continuous for $ 0¥leqq s¥leqq t<¥infty$ and $D(t)$ is an $n¥times n$ matrix continuous for $t$ $¥geqq 0$ . In case $A$ is a stable matrix, there exists a symmetric positive definite matrix $B$ such that (1.4) $A^{T}B+BA=-I$ , and we can use the function $V=x^{T}Bx$ as a Liapunov function to investigate asymptotic behaviors of solutions of (1.2) $(¥mathrm{c}.¥mathrm{f}. [6, 12])$. For the equation (1.3) there is another method, that is, we can use a nice resolvent $Z(t)$ for (1.3)

T Yoneyama

Papers

Asymptotic stability criteria for nonlinear volterra integro-differential equations