1Department of Mathematics, Faculty of Science, Hiroshima University, Higashi- Hiroshima 739-8526 2Department of Mathematics, Faculty of Science, Hiroshima University, Higashi- Hiroshima 739-8526,
Acta mathematica Universitatis Comenianae, Tome 86 (2017) no. 1, pp. 23-50
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N. Yoshida; T. Kusano; N. Yoshida; T. Kusano. Existence and qualitative behavior of oscillatory solutions of second order linear ordinary differential equations. Acta mathematica Universitatis Comenianae, Tome 86 (2017) no. 1, pp. 23-50. http://geodesic.mathdoc.fr/item/AMUC_2017_86_1_a2/
@article{AMUC_2017_86_1_a2,
author = {N. Yoshida and T. Kusano and N. Yoshida and T. Kusano},
title = { Existence and qualitative behavior of oscillatory solutions of second order linear ordinary differential equations},
journal = {Acta mathematica Universitatis Comenianae},
pages = {23--50},
year = {2017},
volume = {86},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_2017_86_1_a2/}
}
TY - JOUR
AU - N. Yoshida
AU - T. Kusano
AU - N. Yoshida
AU - T. Kusano
TI - Existence and qualitative behavior of oscillatory solutions of second order linear ordinary differential equations
JO - Acta mathematica Universitatis Comenianae
PY - 2017
SP - 23
EP - 50
VL - 86
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_2017_86_1_a2/
ID - AMUC_2017_86_1_a2
ER -
%0 Journal Article
%A N. Yoshida
%A T. Kusano
%A N. Yoshida
%A T. Kusano
%T Existence and qualitative behavior of oscillatory solutions of second order linear ordinary differential equations
%J Acta mathematica Universitatis Comenianae
%D 2017
%P 23-50
%V 86
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2017_86_1_a2/
%F AMUC_2017_86_1_a2
We consider the second order linear differential equation(A) (p(t)y′)′ + q(t)y = 0;which is oscillatory, under the assumption that p(t) and q(t) are positive, continuously differentiable and monotone functions on [0;1). After studying qualitative properties, including amplitudes and slopes, of oscillatory solutions, we establish the existence of three types of solutions of (A) referred to as moderately bounded, small of large oscillatory solutions. Essential use is made of pairs of quadratic forms P(t)y′(t)2 + Q(t)y(t)2, R(t)y′(t)2 + S(t)y(t)2, which are monotone for all possible solutions y(t) of (A) but have different monotonicity.
