Existence of Positive Periodic Solutions for Nonautonomous Delay Differential Equations Based on Multiple Integral Approximation
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This paper mainly discusses the existence of positive periodic solutions of hysteretic differential equations approximated by multiple integrals. Delay differential equations play an important role in the modeling of stochastic phenomena, which cannot be replaced by traditional deterministic models. Under some conditions, the trivial solution of the state-dependent time-delay system is exponentially stable if and only if the zero solution of the corresponding linear system is exponentially stable. The asymptotic behavior of solutions of delay differential equations is appropriate in different ranges. A sufficient condition for the existence of a positive periodic solution is studied. The existence of multi-periodic positive solutions for a class of non-autonomous delay differential equations is studied. When general results are applied to several kinds of bio-mathematical models with time-delay, they have high parallelism, high nonlinearity and good fault tolerance. It is of great theoretical and practical significance to study its development process and problems.
Multiple Integral Approximation, Delay Differential Equations, Positive Periodic Solutions