On parameter classes of solutions of the quasilinear second order differential equation

The quasilinear second order differential equation .. x + (1 + p (x, t)) . x + p (x, t) x = f (x, t) where p, f ∈ C (D,R) , D = Ix×I, Ix ⊆ R open set, I = 〈 t,∞ 〉 is under consideration. The paper presents some results on the existence and behavior of parameter classes of solutions of this equation. The qualitative analysis theory and topological retraction method are used. The general results are presented and subsequently certain examples are considered.