On Quasimonotone Increasing Systems of Ordinary Differential Equations

Gerd Herzog

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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