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Boundedness and stability properties of solutions of certain fourth order differential equations via the intrinsic method. (English) Zbl 0868.34039

Summary: Firstly a Lyapunov function is derived for

x (4) +ϕ(x ¨)x +f(x,x ˙)x ¨+g(x ˙)+h(x)=P(t,x,x ˙,x ¨,x )(*)

by applying the intrinsic method introduced by P. S. M. Chin [Int. J. Control 48, No. 4, 1561-1567 (1988; Zbl 0653.93038)]. Secondly equation (*) is examined in two cases: (i) P0, (ii) P¬0. For case (i) the asymptotic stability in the large of the trivial solution x=0 is investigated and for case (ii) boundedness results are obtained for solutions of equation (*). These results improve and include several well-known results.

MSC:
34D20Stability of ODE