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On positive periodic solutions to second-order differential equations with a sub-linear non-linearity
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SYSNO ASEP 0531880 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On positive periodic solutions to second-order differential equations with a sub-linear non-linearity Author(s) Lomtatidze, Alexander (MU-W) RID, SAI, ORCID
Šremr, J. (CZ)Article number 103200 Source Title Nonlinear Analysis: Real World Applications. - : Elsevier - ISSN 1468-1218
Roč. 57, February (2021)Number of pages 24 s. Language eng - English Country GB - United Kingdom Keywords existence ; periodic solution ; positive solution ; second-order differential equation Subject RIV BA - General Mathematics OECD category Pure mathematics Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000573216300006 EID SCOPUS 85089522482 DOI 10.1016/j.nonrwa.2020.103200 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2022 Electronic address https://doi.org/10.1016/j.nonrwa.2020.103200
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