Stability and Boundedness of Solutions of Certain Non-Autonomous Third Order Nonlinear Differential Equations

In this paper, by defining an appropriate Lyapunov functional, we obtain sufficient conditions for which all solutions of certain real non-autonomous third order nonlinear differential equations are asymptotically stable and bounded. The results obtained improve and extend some known results in the literature.

ON THE BOUNDEDNESS AND THE STABILITY PROPERTIES OF SOLUTION OF CERTAIN FOURTH ORDER DIFFERENTIAL EQUATIONS

This paper investigates equation (1) in twocases:(i)P=0, (ii)P satisfies|P (i,x,y,z,w)<(A+|y|+|z|+|w|)q(t).whereq(t) is a nonnegative function of t. For case (i) the asymptotic stability in the large of the trivial solution x=0 is investigated and for case (ii) the boundedness result is obtained for solutions of equation (1). These results improve and include several well-known results.

ON THE BOUNDEDNESS AND THE STABILITY RESULTS FOR THE SOLUTION OF CERTAIN FOURTH ORDER DIFFERENTIAL EQUATIONS VIA THE INTRINSIC METHOD

In this paper, we first present constructing a Lyapunov function for (1. 1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡ 0,and the boundedness result of the solutions of (1 .1 ) for case p≠0. These results improve sveral well-known results.

ON THE BOUNDEDNESS AND THE STABILITY RESULTS FOR THE SOLUTION OF CERTAIN FIFTH ORDER DIFFERENTIAL EQUATIONS

In this paper,we show the asymptotic stability in the large of the trivial solution x 0 for case p=0 and the boundedness result of solutions(1.1) for case p≠0.The resultobtained here extend the author's results in[3].AMS Classification numbers:34D20,34D99

五阶非线性方程解的稳定性和有界性

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。