Asymptotic behavior of solutions of systems of neutral and convolution equations (Q1268084)

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.