Acta Mathematica Hungarica
Volume/Issue:
Volume 127: Issue 1-2
Eventually positive solutions of first order nonlinear differential equations with a deviating argument
Authors:
T. Sakamoto Hiroshima Nagisa Junior High School Senior High School Kairouyama minami 2-2-1, Saeki-ku Hiroshima 731-5138 Japan

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and
S. Tanaka Okayama University of Science Department of Applied Mathematics, Faculty of Science Ridaichou 1-1 Okayama 700-0005 Japan

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Pages:
17–33
Online Publication Date:
13 Apr 2010
Publication Date:
01 Apr 2010
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-010-9064-3
Keywords:
eventually positive solution; deviating argument; asymptotic behavior; 34K11; 34K12
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Abstract  

The following first order nonlinear differential equation with a deviating argument
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$x'(t) + p(t)[x(\tau (t))]^\alpha = 0$$ \end{document}
is considered, where α > 0, α ≠ 1, p ∈ C[t0; ∞), p(t) > 0 for t ≧ t0, τ ∈ C[t0; ∞), limt→∞τ(t) = ∞, τ(t) < t for t ≧ t0. Every eventually positive solution x(t) satisfying limt→∞x(t) ≧ 0. The structure of solutions x(t) satisfying limt→∞x(t) > 0 is well known. In this paper we study the existence, nonexistence and asymptotic behavior of eventually positive solutions x(t) satisfying limt→∞x(t) = 0.
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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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