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DIBLÍK, J.
Original Title
Long-Time Behavior of Positive Solutions of a Differential Equation with State-Dependent Delay
Type
journal article in Web of Science
Language
English
Original Abstract
Abstract. The long-time behavior of positive solutions of a differential equation with state-dependent delay y'(t) = −c(t)y(t − τ(t, y(t))), where c is a positive coefficient, is considered. Sufficient conditions are given for the existence of positive solutions bounded from below and from above by functions of exponential type. As a consequence, criteria for the existence of positive solutions are derived and their lower bounds are given. Relationships are discussed with the existing results on the existence of positive solutions for delayed differential equations.
Keywords
Long-time behavior; time-dependent delay; exponential estimation of solutions; positive solution; monotone iterative method.
Authors
Released
1. 1. 2020
Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS, PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA
Location
USA
ISBN
1937-1632
Periodical
Discrete and Continuous Dynamical Systems - Series S
Year of study
13
Number
1
State
United States of America
Pages from
31
Pages to
46
Pages count
16
URL
http://www.aimsciences.org/article/doi/10.3934/dcdss.2020002
BibTex
@article{BUT165826, author="Josef {Diblík}", title="Long-Time Behavior of Positive Solutions of a Differential Equation with State-Dependent Delay", journal="Discrete and Continuous Dynamical Systems - Series S", year="2020", volume="13", number="1", pages="31--46", doi="10.3934/dcdss.2020002", issn="1937-1632", url="http://www.aimsciences.org/article/doi/10.3934/dcdss.2020002" }