Two classes of positive solutions of first order functional differential equations of delayed type (Q435049)
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scientific article; zbMATH DE number 6057266
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two classes of positive solutions of first order functional differential equations of delayed type |
scientific article; zbMATH DE number 6057266 |
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Two classes of positive solutions of first order functional differential equations of delayed type (English)
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16 July 2012
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delayed differential equation
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retract method
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positive solution
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dominant solution
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subdominant solution
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asymptotic behavior
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The authors study the equation NEWLINE\[NEWLINE\dot{y}= - f(t,y_t).NEWLINE\]NEWLINE The existence of two classes of positive solutions asymptotically different for \(t\to \infty\) is proved using the retract method. By means of solutions of two auxiliary linear equations with several delays, constructed using upper and lower linear functional estimates of the right-hand side of the equation considered, inequalities for both types of positive solutions are given as well.
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