Monotone iterative technique for second order delayed periodic problem in Banach spaces

The existence results of positive ω-periodic solutions are obtained for the second-order functional differential equation with multiple delays , where is a positive ω-periodic function, is a continuous function which is ω-periodic in t, and are ω-periodic functions. The existence conditions concern the first eigenvalue of the associated linear periodic boundary problem. Our discussion is based on the fixed-point index theory in cones.

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On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays

and Applied Analysis Compactness Conditions in the Theory of Nonlinear Differential and Integral Equations Guest Editors: Jozef Banaś, Mohammad Mursaleen, Beata Rzepka, and Kishin Sadarangani

/pdf/compactness-conditions-in-the-theory-of-nonlinear-1v7m3b9roa.pdf

Compactness Conditions in the Theory of Nonlinear Differential and Integral Equations

The existence results of positive -periodic solutions are obtained for the third-order ordinary differential equation with delays where is -periodic function and is a continuous function which is -periodic in are positive constants. The discussion is based on the fixed-point index theory in cones.

/pdf/positive-periodic-solutions-of-third-order-ordinary-31wvrbmt02.pdf

Positive Periodic Solutions of Third-Order Ordinary Differential Equations with Delays

This paper deals with the existence of positive ω-periodic solutions for nth-order ordinary differential equation with delays in Banach space E of the form $$L_{n}u(t)=f\bigl(t,u(t-\tau_{1}),\ldots,u(t- \tau_{m})\bigr),\quad t\in\mathbb{R}, $$ where $L_{n}u(t)=u^{(n)}(t)+\sum_{i=0}^{n-1}a_{i} u^{(i)}(t)$ is the nth-order linear differential operator, $a_{i}\in\mathbb {R}$ ($i=0,1,\ldots,n-1$) are constants, $f: \mathbb{R}\times E^{m}\rightarrow E$ is a continuous function which is ω-periodic with respect to t, and $\tau_{i}>0$ ($i=1,2,\ldots,m$) are constants which denote the time delays. We first prove the existence of ω-periodic solutions of the corresponding linear problem. Then the strong positivity estimation is established. Finally, two existence theorems of positive ω-periodic solutions are proved. Our discussion is based on the theory of fixed point index in cones.

/pdf/positive-periodic-solutions-for-high-order-differential-4qyzmstet9.pdf

Positive periodic solutions for high-order differential equations with multiple delays in Banach spaces

The existence results of positive ω-periodic solutions are obtained for the second-order differential equation with delays , where is a ω-periodic function, is a continuous function, which is ω-periodic in , and are positive constants. Our discussion is based on the fixed point index theory in cones.

/pdf/positive-periodic-solutions-of-second-order-differential-4idwelpquy.pdf

Yongxiang Li

Papers

Positive Periodic Solutions of Second-Order Differential Equations with Delays