Boundedness and Uniqueness of Solutions to Dynamic Equations on Time Scales
نویسندگان
چکیده
subject to the initial condition xðt0Þ 1⁄4 x0; t0 $ 0; x0 [ R; ð2Þ where f : 1⁄20;1Þ £ R ! R is a continuous function and t is from a so-called “time scale” T (which is a nonempty closed subset of R). Equation (1) subject to Eq. (2) is known as an initial value problem (IVP) on time scales. If T 1⁄4 R then x 1⁄4 x 0 and Eqs. (1) and (2) become the following IVP for ordinary differential equations x 0 1⁄4 f ðt; xÞ; t $ 0; ð3Þ xðt0Þ 1⁄4 x0; t0 $ 0: ð4Þ
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