Construction of asymptotic solutions of linear singularly disturbed second-order system with degenerations - Yakovets , V. P. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
The paper discusses the asymptotic behavior of the general solution of a linear singularly perturbed system$ε ^{2h} A(t,ε )\frac{{d^2 x}}{{dt^2 }} + ε ^h B(t,ε )\frac{{dx}}{{dt^2 }} + C(t,ε )x = 0,$ where x∈Rn, t∈[t0; T], h∈N, ε∈ (0, ε0], ε≪1 and det A(t, 0) ≡ 0. It is assumed that the quadratic pencil of matrices C(t, 0) + λB(t, 0) + λ2A(t, 0) is regular and has either simple “finite” and “infinite” elementary divisors or just one multiple elementary divisor.