Publication detail

On a structure of the set of positive solutions to second-order equations with a super-linear non-linearity

ŠREMR, J.

Original 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

English

Original Abstract

We study the existence and multiplicity of positive solutions to the periodic problem $$ u '' = p(t)u - q(t, u)u + f(t);\quad u(0) = u(\omega),\ u'(0) = u'(\omega), $$ where $p,f$ is an element of $L([0,\omega])$ and $q: [0,\omega] \times R\to R$ 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

Periodic solution;second-order differential equation;super-linear non-linearity;existence;positive solution;minimal positive solution

Authors

ŠREMR, J.

Released

1. 2. 2022

ISBN

1072-947X

Periodical

Georgian Mathematical Journal

Year of study

29

Number

1

State

Federal Republic of Germany

Pages from

139

Pages to

152

Pages count

14

URL

https://www.degruyter.com/document/doi/10.1515/gmj-2021-2117/html

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",
  journal="Georgian Mathematical Journal",
  year="2022",
  volume="29",
  number="1",
  pages="139--152",
  doi="10.1515/gmj-2021-2117",
  issn="1072-947X",
  url="https://www.degruyter.com/document/doi/10.1515/gmj-2021-2117/html"
}