On ordinary differential equations with quasimonotone increasing right-hand side

被引：4

作者：

Herzog, G ^{[1
]}

机构：

[1] Univ Karlsruhe, Inst Math 1, D-76128 Karlsruhe, Germany

来源：

ARCHIV DER MATHEMATIK | 1998年 / 70卷 / 02期

关键词：

Differential Equation; Banach Space; Ordinary Differential Equation; Lipschitz Condition; Order Banach Space;

D O I：

10.1007/s000130050177

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the initial value problem x'(t) = f(t,x(t)), t is an element of [0,T], x(0) = x(0), is uniquely solvable in certain ordered Banach spaces if, f is quasimonotone increasing with respect to x, and if f is satisfying a one-sided Lipschitz condition with respect to the order-inducing cone.

引用

页码：142 / 146

页数：5

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