
doi: 10.1137/0129036
In this paper we present a number of results on perturbations of second order differential equations of the form $x'' + f( x )h( {x'} )x' + g( x ) = 0$. This is accomplished by constructing a variety of Lyapunov functions. We then show how these Lyapunov functions can be converted to Lyapunov functionals for the delay equation $x'' + f( x )h( {x'} )x' + g( {x( {t - \tau ( t )} )} ) = 0$, thereby obtaining boundedness results. Some of the work is generalized to higher order systems. We also present some continuation results for higher order delay equations. Several examples are given.
Stability theory of functional-differential equations, Perturbations of ordinary differential equations, Stability of solutions to ordinary differential equations, Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
Stability theory of functional-differential equations, Perturbations of ordinary differential equations, Stability of solutions to ordinary differential equations, Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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