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Asymptotic and oscillatory behaviour of solutions of a linear differential equation. (English) Zbl 0764.34027
The linear differential equation (*)y (n) +p(t)y (k) +q(t)y=0 is considered, where n,k are integers, n>1, 1k<n, p(t), q(t) are continuous together with some derivatives. The aim of this paper is to derive the oscillatory properties of a fundamental system of solutions of (*) on the base of the asymptotic behaviour of (*) in the author’s previous paper [Arch. Math., Brno 22, 193-202 (1986; Zbl 0607.34051)]. The basic suppositions here are q '' (t)q(t) -1-1/2n L[a,), p(t)q(t) -1+(k+1)/n L[a,b) for n even and similar ones for n odd. L[a,) denotes the set of Lebesgue integrable complex-valued functions in [a,).
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34D05Asymptotic stability of ODE
34A30Linear ODE and systems, general