General Permanence Conditions for Nonlinear Difference Equations of Higher Order
نویسندگان
چکیده
w . m w . w . where f : 0, ` a 0, ` and the initial values x , . . . , x g 0, ` . 0 1ym Ž . In studying the global behavior of the solutions of Eq. 1 , we often need Ž . to establish that 1 is permanent, i.e., it has the property that every one of its solutions is eventually confined within a fixed compact interval regardless of the initial values chosen. Permanence is needed directly or indirectly in establishing other properties such as persistent bounded oscillaw x tions or the global attractivity of fixed points. For example, in 6 permanence of the equation
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