Positive periodic solutions to super-linear second-order ODEs

Jiří Šremr

Czechoslovak Mathematical Journal (2025)

  • Issue: 1, page 257-275
  • ISSN: 0011-4642

Abstract

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We study the existence and uniqueness of a positive solution to the problem u ' ' = p ( t ) u + q ( t , u ) u + f ( t ) ; u ( 0 ) = u ( ω ) , u ' ( 0 ) = u ' ( ω ) with a super-linear nonlinearity and a nontrivial forcing term f . To prove our main results, we combine maximum and anti-maximum principles together with the lower/upper functions method. We also show a possible physical motivation for the study of such a kind of periodic problems and we compare the results obtained with the facts well known for the corresponding autonomous case.

How to cite

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Šremr, Jiří. "Positive periodic solutions to super-linear second-order ODEs." Czechoslovak Mathematical Journal (2025): 257-275. <http://eudml.org/doc/299901>.

@article{Šremr2025,
abstract = {We study the existence and uniqueness of a positive solution to the problem \[ u^\{\prime \prime \}=p(t)u+q(t,u)u+f(t);\quad u(0)=u(\omega ),\ u^\{\prime \}(0)=u^\{\prime \}(\omega ) \] with a super-linear nonlinearity and a nontrivial forcing term $f$. To prove our main results, we combine maximum and anti-maximum principles together with the lower/upper functions method. We also show a possible physical motivation for the study of such a kind of periodic problems and we compare the results obtained with the facts well known for the corresponding autonomous case.},
author = {Šremr, Jiří},
journal = {Czechoslovak Mathematical Journal},
keywords = {second-order differential equation; super-linearity; positive solution; existence; uniqueness},
language = {eng},
number = {1},
pages = {257-275},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Positive periodic solutions to super-linear second-order ODEs},
url = {http://eudml.org/doc/299901},
year = {2025},
}

TY - JOUR
AU - Šremr, Jiří
TI - Positive periodic solutions to super-linear second-order ODEs
JO - Czechoslovak Mathematical Journal
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 257
EP - 275
AB - We study the existence and uniqueness of a positive solution to the problem \[ u^{\prime \prime }=p(t)u+q(t,u)u+f(t);\quad u(0)=u(\omega ),\ u^{\prime }(0)=u^{\prime }(\omega ) \] with a super-linear nonlinearity and a nontrivial forcing term $f$. To prove our main results, we combine maximum and anti-maximum principles together with the lower/upper functions method. We also show a possible physical motivation for the study of such a kind of periodic problems and we compare the results obtained with the facts well known for the corresponding autonomous case.
LA - eng
KW - second-order differential equation; super-linearity; positive solution; existence; uniqueness
UR - http://eudml.org/doc/299901
ER -

References

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