In the paper, conditions are obtained, in terms of coefficient functions, which are necessary as well as sufficient for non-oscillation/oscillation of all solutions of self-adjoint linear homogeneous equations of the form ∆(pn−1∆yn−1) + qyn = 0, n ≥ 1, where q is a constant. Sufficient conditions, in terms of coefficient functions, are obtained for non-oscillation of all solutions of nonlinear non-homogeneous equations of the type ∆(pn−1∆yn−1) + qng(yn) = fn−1, n ≥ 1, where, unlike earlier works, fn > 0 or 6 0 (but 6≡ 0) for large n. Further, these results are used to obtain sufficient conditions for non-oscillation of all solutions of forced linear third order difference equations of the form yn+2 + anyn+1 + bnyn + cnyn−1 = gn−1, n ≥ 1.
The aim of this article is to present a specific method for the study of the life-course, which focuses on life-course trajectories as a whole through the use of sequence analysis. In the first part, two approaches for the quantitative analysis of the life-course are distinguished: an event-oriented perspective and a trajectory-based (holistic) perspective. The holistic perspective is based on sequence analysis and more specifically on optimal matching. The trajectory-based perspective does not focus on single life events, but on whole sequences of events. In the second part, using the Czech wave of the ISSP 2002 dataset, which includes partnership and family histories, this article presents several examples of the use of sequence analysis of family trajectories. This study shows that sequence analysis can help identify patterns associated with typical and distinctive life-course trajectories., Jana Chaloupková., and Obsahuje bibliografii a bibliografické odkazy