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Existence and multiplicity of periodic solutions to indefinite singular equations having a non-monotone term with two singularities
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SYSNO ASEP 0504396 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Existence and multiplicity of periodic solutions to indefinite singular equations having a non-monotone term with two singularities Author(s) Hakl, Robert (MU-W) RID, SAI, ORCID
Zamora, M. (ES)Source Title Advanced Nonlinear Studies. - : Walter de Gruyter - ISSN 1536-1365
Roč. 19, č. 2 (2019), s. 317-332Number of pages 16 s. Language eng - English Country DE - Germany Keywords indefinite weight ; periodic solution ; singular differential equation Subject RIV BA - General Mathematics OECD category Applied mathematics Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000465562200004 EID SCOPUS 85048113744 DOI 10.1515/ans-2018-2018 Annotation Efficient conditions guaranteeing the existence and multiplicity of T-periodic solutions to the second order differential equation u ′′ = h (t)g(u) are established. Here, g : ( A , B ) → (0, + ∞) is a positive function with two singularities, and h ϵ L (ℝ/T ℤ) is a general sign-changing function. The obtained results have a form of relation between multiplicities of zeros of the weight function h and orders of singularities of the nonlinear term. Our results have applications in a physical model, where from the equation u ′′ = h(t) sin2 u one can study the existence and multiplicity of periodic motions of a charged particle in an oscillating magnetic field on the sphere. The approach is based on the classical properties of the Leray-Schauder degree. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2020 Electronic address http://dx.doi.org/10.1515/ans-2018-2018
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