Asymptotic stability for ordinary differential systems with time-dependent restoring potentials (Q1912917)

The authors study the equation \[ (\nabla_p G(u,u'))'- \nabla_u G(u,u')+ q^m(t)f(u)= Q(t,u,u'),\tag{1} \] a generalization of \(u''+h(t)u'+ q^2(t)f(u)= Q(t,u,u')\). Their main results, which are too lengthy to quote here, give sufficient conditions that bounded solutions of (1) tend to 0 as \(t\to\infty\). Several previous results are corollaries of their main theorems. Applications are given to holonomic mechanical systems and to Matukama type equations.