期刊论文

Oscillatory and Asymptotic Behavior of Third-order Nonlinear Neutral Differential Equations

中文

应用数学学报

0254-3079

2021

44

04

508-521

湖南省自然科学基金项目（2019JJ40004）； 湖南省教育厅科学基金重点项目（20A063）； 湖南省双一流应用特色学科项目（湘教通[2018]469）； 湖南省科技创新计划项目（2016TP1020）资助；

本校为第一机构

本文的目的是研究三阶非线性中立型连续分布时滞微分方程$${\left( {r\left( t \right){{\left[ {{{\left( {x\left( t \right) + \int_a^b {p\left( {t,\xi } \right)x\left( {\tau \left( {t,\xi } \right)} \right){\rm{d}}\xi } } \right)}^{\prime \prime }}} \right]}^\alpha }} \right)^\prime } + \int_c^d {q\left( {t,\xi } \right)f\left( {x\left( {\sigma \left( {t,\xi } \right)} \right)} \right)} {\rm{d}}\xi = 0$$解的振动性和渐近性,其中$\frac{{f\left( x \right)}}{{{x^\beta }}} \ge \delta > 0$,$x \ne 0$且$\alpha > 0$和$\beta > 0$均为正奇数之商.利用广义Riccati变...

The objective of this paper is to study oscillatory and asymptotic behaviors of solutions of a class of third-order nonlinear neutral differential equations with continuously distributed delay $${\left( {r\left( t \right){{\left[ {{{\left( {x\left( t \right) + \int_a^b {p\left( {t,\xi } \right)x\left( {\tau \left( {t,\xi } \right)} \right){\rm{d}}\xi } } \right)}^{\prime \prime }}} \right]}^\alpha }} \right)^\prime } + \int_c^d {q\left( {t,\xi } \right)f\left( {x\left( {\sigma \left( {t,\xi } \right)} \right)} \right)} {\rm{d}}\xi = 0,$$ where $\frac{{f\left( x \right)}}{{{x^\beta }}} \ge \del...