拟线性泛函微分方程组的Cauchy问题
Cauchy problem for quasilinear systems of functional differential equations
摘要：
本文利用压缩映射原理证明了具有滞后变元的拟线性泛函微分方程组的Cauchy问题在适当的限制条件下存在唯一解。由此得到了具有局部可积系数和局部可测滞后变元的线性泛函微分方程组的Cauchy问题存在唯一解.我们证明了具有超前变元的拟线性泛函微分方程组的Cauchy问题也可以得到类似的结果。
英文摘要：
We use the contracting mapping principle for proving that under some mild restrictions the Cauchy problem for quasilinear systems of functional differential equations with retarded arguments has the unique solution. As a consequence from this result we obtain that the Cauchy problem for linear systems of functional differential equations with locally integrable coeffcients and with locally measurable retarded arguments has the unique solution. We show that similar results can be obtained for the Cauchy co problem of quasilinear systems of functional differential equations with advanced arguments.
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