On positive periodic solutions to second-order differential equations with a sub-linear non-linearity

0531880 - MÚ 2022 RIV GB eng J - Journal Article
Lomtatidze, Alexander - Šremr, J.
On positive periodic solutions to second-order differential equations with a sub-linear non-linearity.
Nonlinear Analysis: Real World Applications. Roč. 57, February (2021), č. článku 103200. ISSN 1468-1218. E-ISSN 1878-5719
Institutional support: RVO:67985840
Keywords : existence * periodic solution * positive solution * second-order differential equation
OECD category: Pure mathematics
Impact factor: 2.765, year: 2021
Method of publishing: Limited access
https://doi.org/10.1016/j.nonrwa.2020.103200

The paper studies the existence and uniqueness of a positive periodic solution to the equation u′′=p(t)u−q(t,u), where p∈L([0,ω]) and q:[0,ω]×R→R is a Carathéodory function sub-linear in the second argument. The general results are applied to some particular cases such as the equation u′′=p(t)u−h(t)sinu with p,h∈L([0,ω]). This equation appears when approximating non-linearities in the equation of motion of a certain non-linear oscillator, namely, a pendulum deflected towards the two charged bodies.
Permanent Link: http://hdl.handle.net/11104/0310518