高阶变系数函数方程解的振动准则

吴英柱

doi:10.6054/j.jscnun.2015.08.024

高阶变系数函数方程解的振动准则

吴英柱^,

（广东石油化工学院数学系,茂名 525000）

基金项目:

国家自然科学基金项目（1127380）;茂名市科技计划项目（2014050）;广东石油化工学院自然科学研究基金项目（513021）

详细信息

作者简介:
吴英柱，讲师，Email：wuyingzhu1978@163.com.

通讯作者:
吴英柱，讲师，Email：wuyingzhu1978@163.com.

中图分类号: O175.1
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出版历程
- 收稿日期: 2015-06-30
- 刊出日期: 2016-03-24

Oscillation Criteria of Solutions to Higher Order Variable Coefficient Functional Equations

WU Yingzhu*^,

(Department of Mathematics,Guangdong University of Petrochemical Technology,Maoming 525000,China)

摘要

摘要: 利用反复迭代的思想方法，讨论了一类高阶变系数函数方程x(g(t))=p(t)x(t)+〖DD(〗m〖〗i=1〖DD)〗Q_i(t)〖DD(〗s〖〗j=1〖DD)〗〖JB(|〗x(gk_j+i(t))〖JB)|〗a_jsgnx(gk_j+i(t))解的振动性，给出了这类函数方程一切解振动的几个充分条件：如果存在整数n0，使得lim〖DD(X〗t〖DD)〗sup〖DD(〗m〖〗i=1〖DD)〗Qi(t)〖DD(〗s〖〗j=1〖DD)〗〖JB2*［〗〖DD(〗kj+i-1〖〗k=1〖DD)〗p(gk(t))〖JB2*］〗aj1〖KG1.5mm〗(t〖XC152HSW1.TIF；%85%85,JZ〗I),则上述方程的一切解振动；如果存在一个整数n0，使得lim〖DD(X〗t〖DD)〗sup〖JB2*［〗p(g(t))〖DD(〗m〖〗i=1〖DD)〗Qi(t)〖DD(〗s〖〗j=1〖DD)〗〖JB2*［〗〖DD(〗kj+i-2〖〗k=1〖DD)〗pn(gk(t))〖JB2*］〗j+〖DD(〗m〖〗i=1〖DD)〗Qi(g(t))〖DD(〗s〖〗j=1〖DD)〗〖JB2*［〗〖DD(〗kj+i〖〗k=2〖DD)〗pn(gk(t))〖JB2*］〗j〖JB2*］〗1〖KG1.5mm〗(t〖XC152HSW1.TIF；%85%85,JZ〗I),则上述方程的一切解也振动. 并且给出了该方程在差分方程中的若干应用.
- 高阶 /
- 函数方程 /
- 非线性 /
- 振动
Abstract: By utilizing iterative method, oscillation of solutions to high-order variable coefficient functional differential equations of the form x(g(t))〖KG-*4〗=p(t)x(t)+〖DD(〗m〖〗i=1〖DD)〗Qi(t)〖DD(〗s〖〗j=1〖DD)〗〖JB(|〗x(gk_j+i(t))〖JB)|〗ajsgn x(gkj+i(t)) is discussed. When n0, n is an integer, and lim〖DD(X〗t〖DD)〗sup〖DD(〗m〖〗i=1〖DD)〗Qi(t)〖DD(〗s〖〗j=1〖DD)〗〖JB2*［〗〖DD(〗kj+i-1〖〗k=1〖DD)〗p(gk(t))〖JB2*］〗aj1〖KG0.8mm〗(t〖XC152HSW1.TIF；%85%85,JZ〗I), all the solutions of the above equations are oscillation. When n0, n is an integer, and lim〖DD(X〗t〖DD)〗sup〖JB2*［〗p(g(t))〖DD(〗m〖〗i=1〖DD)〗Qi(t)〖DD(〗s〖〗j=1〖DD)〗〖JB2*［〗〖DD(〗kj+i-2〖〗k=1〖DD)〗pn(gk(t))〖JB2*］〗j+〖DD(〗m〖〗i=1〖DD)〗Qi(g(t))〖DD(〗s〖〗j=1〖DD)〗〖JB2*［〗〖DD(〗kj+i〖〗k=2〖DD)〗pn(gk(t))〖JB2*］〗j〖JB2*］〗1〖KG1.5mm〗(t〖XC152HSW1.TIF；%85%85,JZ〗I), all the solutions of the above equations are oscillation. Some sufficient conditions for these equations are established. Some applications in difference equations are given.
- higher-order /
- functional equations /
- nonlinear /
- oscillation