On the asymptotic stability of solutions of a second order nonlinear differential equation (Q1100333)

Consider the equation \((1)\quad (r(t)x')'+f(t,x,x')x'+p(t)g(t)=0,\) where p and r are continuously differentiable, positive functions on \(R^+\), \(f: R^+\times R\to R^+\) is a continuous function, \(g: R\to R\) is a continuous function such that \(xg(x)>0\) (x\(\neq 0)\). The authors give the sufficient conditions respectively for the (globally) asymptotic stability, (globally) equi-asymptotic stability, and (globally) uniformly stability of the zero solution of (1).