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"
}