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In this paper, we discuss the problem of stability of Volterra integrodifferential equation $$\dot x = A(t)x + \int_0^t {C(t,s)} x(s)ds$$ with the decomposition $$\begin{gathered} \dot x_i = A_{ii} (t)x_i + \sum\limits_{\mathop {i = 1}\limits_{j \ne i} }^r {A_{ij} (t)x_j + \int_0^t {\left[ {C_{ii} (t,s)x_i (s) + \sum\limits_{\mathop {j = 1}\limits_{j \ne i} }^r {C_{ij} (t,s)x_j (s)} } \right]} ds,} \hfill \\ i = 1,2, \cdot \cdot \cdot ,r, \hfill \\ \end{gathered} $$ wherex ∈R n,x T=(x 1 T , ...,x r/T),x i ∈R ni and ∑ i=1 r n i=n;A(t)=(A ij(t)) in whichA ij(t) (i,j=1, ...,r) is ann i ×n j matrix of functions continuous for 0 ≤t<∞;C(t,s)=(C ij (t,s,)) in whichC ij(t,s)(i,j=1, ...,r) is ann i ×n j matrix of functions continuous for 0≤s≤t<∞.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 13, 2005
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