ASYMPTOTIC STABILITY AND BOUNDEDNESS CRITERIA FOR CERTAIN SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS

ASYMPTOTIC STABILITY AND BOUNDEDNESS CRITERIA

Abstract

In this paper, we examined some criteria for the stability and boundedness of solutions to certain second order nonlinear differential equation
$$x^{\prime\prime} + b(t)f(x,x^\prime) + c(t)g(x)h(x^\prime) = p(t,x,x^\prime),$$
where $b,c,f,g,h$ and $p$ are real valued functions which depend on the argument displayed explicitly. By applying a suitable Lyapunov function to study the qualitative properties mentioned earlier, we are able to extablish the asymptotic stability and boundedness of solutions. An example on the stability of solutions is hereby included to corroborate our result.