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We give a theorem on error estimates of approximate solutions for explicit and implicit difference functional equations with unknown functions of several variables. We apply this general result to investigate the stability of difference methods for quasilinear functional differential equations with initial boundary condition of Dirichlet type. We consider first order partial functional differential equations and parabolic functional differential problems. We compare the properties of explicit...
We give existence theorems for weak and strong solutions with trichotomy of the nonlinear differential equation
where is a family of linear operators from a Banach space into itself and . By we denote the space of linear operators from into itself. Furthermore, for and , we let be the Banach space of continuous functions from into and . Let be a strongly measurable and Bochner integrable operator on and for define for each . We prove that, under certain conditions,...
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