Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations
Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations
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DOI：
10.1155/s1687183904310022
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发表时间：
2004-12
影响因子：
4.1
通讯作者：
A. Cabada;D. R. Vivero
中科院分区：
文献类型：
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作者：
A. Cabada;D. R. Vivero
我们证明了在时间尺度上一般n阶问题的耦合上下解的存在性和唯一性，其中i = 1，2，.，n线性依赖于i阶Δ-导数，以及反周期边值条件.这里方程的非线性右端由函数f（t，x）定义，该函数在t中是rd连续的，并且在t中在x中一致连续。为此，我们得到了反周期函数空间中一个相关线性算子的绿色函数的表达式。
We prove existence and uniqueness results in the presence of coupled lower and upper solutions for the general n th problem in time scales with linear dependence on the i th Δ-derivatives for i = 1,2,…,n, together with antiperiodic boundary value conditions. Here the nonlinear right-hand side of the equation is defined by a function f(t,x) which is rd-continuous in t and continuous in x uniformly in t. To do that, we obtain the expression of the Green's function of a related linear operator in the space of the antiperiodic functions.