Stability results for the solutions of certain fourth-order autonomous differential equations

Abstract

Lyapunov functions have been derived for various authors to study the stability of solutions for certain fourth-order non-linear autonomous differential equations. Cartwright (1956) has studied (1) and (2) applying the method of analogy with linear systems, Ku (1964) has proposed a matrix method to study (3) and Skidmore (1966) has derived another Lyapunov function for (1) applying an extension to the method proposed by Leighton (1963). The intrinsic method proposed by Chin (1988 a, b) is applied to derive the Lyapunov functions obtained by Cartwright, Ku and Skidmore. Further, new Lyapunov functions are derived for (1), (2) and (3) applying the intrinsic method that are shown to be far less restrictive than those obtained by the various authors in the literature.