Vol. 57, No. 1, pp. 35-43 (2000)
On Quasimonotone Increasing Systems of Ordinary Differential Equations
Gerd HerzogMathematisches Institut I, Universität Karlsruhe,
D-76128 Karlsruhe - GERMANY
Abstract: We prove an uniqueness theorem for the initial value problem $x'(t)=f(t,x(t))$, $x(t_0)=x_0$, in case that $f$ is quasimonotone increasing with respect to an arbitrary cone, and is satisfying a one-sided Lipschitz condition with respect to a single linear functional. An inequality concerning the difference of solutions is obtained.
Keywords: Systems of differential equations; quasimonotone increasing functions; one-sided estimates.
Classification (MSC2000): 34C11.
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Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.