Sharp conditions for existence of nontrivial invariant cones of nonnegative initial values of difference equations
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摘要
It is proved that an arbitrary scalar difference equation has a nontrivial invariant cone in the set of the nonnegative initial values if and only if the associated characteristic equation has a positive root. By using this fact, there is given a construction of the maximal invariant cone in the set of nonnegative initial values via a positive root of the associated characteristic equation. Finally, the present results are compared with some earlier ones which were obtained for delay differential equations in the same direction.
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论文评审过程:Available online 22 March 2002.
论文官网地址:https://doi.org/10.1016/0096-3003(90)90014-T