Affiliation:
1. 1 Shimane University Department of Mathematics and Computer Science Matsue 690-8504 Japan
Abstract
This paper is concerned with the asymptotic behavior of solutions of a class of second-order half-linear differential equations of the form (
ϕp
(
ẋ
))
.
+
a
(
t
)
ϕp
(
ẋ
) +
b
(
t
)
ϕp
(
x
) = 0. The main purpose of this paper is to answer the question of how every solution approaches zero, under the assumption that the zero solution is globally asymptotically stable. Sufficient conditions are also given for the zero solution to be globally asymptotically stable. Moreover, an autonomous case is investigated in full detail and a geometrical classification is made based on the asymptotic behavior of solutions. The method used here is mainly phase plane analysis for a system equivalent to the half-linear differential equations. Some suitable examples are included to illustrate the main results. Global phase portraits are also attached for a deeper understanding.
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