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Forced oscillation and asymptotic behavior of solutions of linear differential equations of second order

Shoukaku Yutaka

Opuscula Mathematica

2022

Vol. 42, no. 6

867--885

The paper deals with the second order nonhomogeneous linear differential equation (p(t)y′(t))′ + q(t)y(t) = f(t), which is oscillatory under the assumption that p(t) and q(t) are positive, continuously differentiable and monotone functions on [0,∞). Throughout this paper we shall use pairs of quadratic forms, which obtained by different methods than Kusano and Yoshida. This form will lead to a property of qualitative behavior, including amplitudes and slopes, of oscillatory solutions of the above equation. In addition, we will discuss the existence of three types (moderately bounded, small, large) of oscillatory solutions, which are based on results due to Kusano and Yoshida.

Oscillation criteria for higher order differential equations with positive and negative coefficients

Shoukaku Yutaka

Fasciculi Mathematici

2019

nr 62

121--140

A new sufficient conditions for the oscillation of all solutions of higher order neutral delay differential equations with positive and negative coefficients are given. Because, we did not find a paper which gave conditions to guarantee the existence of oscillatory solutions for those equations with positive and negative coefficients. The main distinguishing feature of results is oscillation theorems for all solutions of those homogeneous or nonhomogeneous neutral equations are derived. These oscillation criteria extend and improve the results given in the recent papers.