摘要
分两种情况研究方程x^(5)+ax^(4)+h((?))+c(?)+g((?))+f(x)=p(t,x,(?),(?),(?),(?)):(Ⅰ)P≡0,(Ⅱ)P(≠0)满足|P(t,x,y,z,w,u)|≤(A+|y|+|z|+|w|+|u|)q(t),其中q(t)是t的非负函数.对第一种情况研究了零解的全局渐近稳定性;对第二种情况给出了解的估计和有界性结果。这些结果推广和改进了若干最近发表的结果。
Studies the fifth order equation x(5) + ax(4)+ h(x) +cx + g(x)+f(x) = P(t , x , x , x , x , x) (1) in the two cases : (Ⅰ) when P= 0 , (Ⅱ) when P(≠ 0) satisfies |P(t , x ,y , z , w , u)|≤(A + |y |+ |z|+ |w |+ |u |)q(t) , where q is a nonnegative function of t . In case (Ⅰ) the asymptotic stability in the large of the solution x = 0 is studied ; in case (Ⅱ) a general estimate and a result concerning the boundedness are deduced for solutions of (1). There results include and improve some recently published results .
出处
《北京理工大学学报》
EI
CAS
CSCD
1991年第3期1-11,共11页
Transactions of Beijing Institute of Technology
基金
国家自然科学基金
关键词
微分方程
全局稳定性
有界性
differential equation
global stability / nonlinear differential equations of fifth order
global asymptotic stability
boundedness
