Necessary and sufficient conditions for the existence and ?-uniqueness of bounded solutions of the equation x′ = f(x) ? h(t) |
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| Authors: | V E Slyusarchuk |
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| Institution: | 1. National University for the Management of Water and Natural Resources, Rivne, Ukraine
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| Abstract: | We introduce the notion of ?-unique bounded solution to the nonlinear differential equation x′ = f(x) ? h(t), where f: ? → ? is a continuous function and h(t) is an arbitrary continuous function bounded on ?. We derive necessary and sufficient conditions for the existence and ?-uniqueness of bounded solutions to this equation. |
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