Existence of the nonoscillatory solutions of higher order neutral dynamic equations on time scales

Advances in Difference Equations

Hongjian Xi¹  Chunyan Tao²  Taixiang Sun² 

[1] College of Information and Statistics, Guangxi University of Finance and Economics, Nanning, China;Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications, Nanning, China

关键词: nonoscillatory solution;    dynamic equation;    time scale;    34K11;    39A10;    39A99;   

DOI  :  10.1186/s13662-015-0621-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we investigate the existence of the nonoscillatory solutions of the following higher order neutral dynamic equation:{rn(t)[(rn−1(t)(⋯(r1(t)(x(t)−q(t)x(τ(t)))Δ)Δ⋯)Δ)Δ]γ}Δ+f(t,x(δ(t)))=0$\{r_{n}(t)[(r_{n-1}(t)(\cdots(r_{1}(t)(x(t)-q(t)x(\tau(t)))^{\Delta })^{\Delta}\cdots)^{\Delta})^{\Delta}]^{\gamma}\}^{\Delta} +f(t,x(\delta (t)))=0$fort∈[t0,∞)T$t\in \left .[t_{0},\infty) \right ._{\mathbb{T}}$, and obtain some necessary and sufficient conditions for the existence of nonoscillatory bounded solutions for this equation.

【 授权许可】

CC BY