TY  - JOUR
ID  - Shoukaku2022
LB  - Shoukaku2022
AU  - Shoukaku, Yutaka
TI  - Forced oscillation and asymptotic behavior of solutions of linear differential equations of second order
ST  - Forced oscillation and asymptotic behavior of solutions of linear differential equations of second order
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2022
VL  - 42
IS  - 6
SP  - 867
EP  - 885
DO  - https://doi.org/10.7494/OpMath.2022.42.6.867
UR  - https://doi.org/10.7494/OpMath.2022.42.6.867
AB  - 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 \([0,\infty)\). 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.
KW  - forced oscillation
KW  - asymptotic behavior
KW  - second order
KW  - differential equation
SN  - 1232-9274
ER  -