Publication detail
On a structure of the set of positive solutions to second-order equations with a super-linear non-linearity
ŠREMR, J.
English title
On a structure of the set of positive solutions to second-order equations with a super-linear non-linearity
Type
journal article in Web of Science
Language
en
Original abstract
We study the existence and multiplicity of positive solutions to the periodic problem u '' = p(t)u – q(t, u)u + f(t); u(0) = u(omega), u'(0) = u'(omega), where p, f is an element of L([0, omega]) and q: [0, omega] x R -> R is a Caratheodory function. By using the method of lower and upper functions, we show some properties of the solution set of the considered problem and, in particular, the existence of a minimal positive solution.
English abstract
We study the existence and multiplicity of positive solutions to the periodic problem u '' = p(t)u – q(t, u)u + f(t); u(0) = u(omega), u'(0) = u'(omega), where p, f is an element of L([0, omega]) and q: [0, omega] x R -> R is a Caratheodory function. By using the method of lower and upper functions, we show some properties of the solution set of the considered problem and, in particular, the existence of a minimal positive solution.
Keywords in English
Periodic solution;second-order differential equation;super-linear non-linearity;existence;positive solution;minimal positive solution
Released
01.02.2022
ISSN
1072-947X
Volume
29
Number
1
Pages from–to
139–152
Pages count
14
BIBTEX
@article{BUT176606,
author="Jiří {Šremr},
title="On a structure of the set of positive solutions to second-order equations with a super-linear non-linearity",
year="2022",
volume="29",
number="1",
month="February",
pages="139--152",
issn="1072-947X"
}