On oscillation, continuation, and asymptotic expansions of solutions of linear differential equations
The paper deals with oscillation criteria of fourth order linear differential equations with quasi-derivatives.
In this paper, necessary and sufficient conditions are obtained for every bounded solution of to oscillate or tend to zero as for different ranges of . It is shown, under some stronger conditions, that every solution of oscillates or tends to zero as . Our results hold for linear, a class of superlinear and other nonlinear equations and answer a conjecture by Ladas and Sficas, Austral. Math. Soc. Ser. B 27 (1986), 502–511, and generalize some known results.
Sufficient conditions are obtained in terms of coefficient functions such that a linear homogeneous third order differential equation is strongly oscillatory.
The paper deals with the oscillation of a differential equation as well as with the structure of its fundamental system of solutions.