ASYMPTOTIC BEHAVIOR OF FUNCTIONAL DYNAMIC EQUATIONS IN TIME SCALE
ASYMPTOTIC BEHAVIOR OF FUNCTIONAL DYNAMIC EQUATIONS IN TIME SCALE
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发表时间：
2010
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通讯作者：
S. Castillo;M. Pinto
中科院分区：
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作者：
S. Castillo;M. Pinto
考虑具有时滞变元的时标线性泛函动力方程（0.1）y（t）= B（t）y（t），t ∈ T ∈ T ∈（0，+∞），其中T是时标R的一个闭子集，在这种情况下没有上界，是de Hilger导数，它统一了序列的差分算子和导数.函数B，λ：T → C，λ> 0是“局部可积的”并且满足积分小性条件，其意义将在后面定义。给出了方程（0.1）解的渐近公式。它们统一和推广了差分和微分方程的渐近公式。
It is considered a scalar linear functional dynamic equation in time scale with delayed argument of the form (0.1) y � (t) = b(t)y(�(t)), t ∈ T ∩ (0,+∞(, where T, the time scale, is a closed subset of R without upper bound for this case, � is de Hilger's derivate, which among other things, unifies difference operator for sequences and the derivate. The functions b,� : T → C, � > 0, are "locally integrable" and satisfy integral smallness conditions in a sense to be defined later. Asymptotic formulas of solutions of equation (0.1) are given. They unify and extend asymptotic formulas of difference and differential equations.