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Asymptotic behavior of solutions of systems of neutral and convolution equations. (English) Zbl 0912.45013

Let \(X\) be a Banach space, \(L(X)\) be the space of all linear bounded operators in \(X\). The authors study asymptotic behavior of solutions of the equation \[ D(\Omega)= \sum_{k=0}^{n}\sum_{j=1}^{m} a_{jk}\Omega^{(k)}(t+t_{j})+ \int_{-\infty }^{\infty }G(s)\Omega(t+s) ds=b(t), \] where \(t_{1}, t_{2},\ldots, t_{m}\in\mathbb{R}\), \(a_{jk}\in L(X)\), \(G\in L^{1}(\mathbb{R}, L(X))\), \(\Omega\) and \(b\) are functions from \(\mathbb{R}\) to \(X\).
Similar equations connected with the semiaxis and systems of convolution operators are also investigated. The investigation leads to an extension of known classes of almost periodic functions.
Reviewer: Vladimir S.Pilidi

MSC:

45N05 Abstract integral equations, integral equations in abstract spaces
45F15 Systems of singular linear integral equations
45M05 Asymptotics of solutions to integral equations
42A75 Classical almost periodic functions, mean periodic functions
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