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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 ASEP0504396
    Document TypeJ - Journal Article
    R&D Document TypeJournal Article
    Subsidiary JČlánek ve WOS
    TitleExistence 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 TitleAdvanced Nonlinear Studies - ISSN 1536-1365
    Roč. 19, č. 2 (2019), s. 317-332
    Number of pages16 s.
    Languageeng - English
    CountryDE - Germany
    Keywordsindefinite weight ; periodic solution ; singular differential equation
    Subject RIVBA - General Mathematics
    OBOR OECDApplied mathematics
    Způsob publikováníOmezený přístup
    Institutional supportMU-W - RVO:67985840
    UT WOS000465562200004
    EID SCOPUS85048113744
    DOI10.1515/ans-2018-2018
    AnnotationEfficient 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.
    WorkplaceMathematical Institute
    ContactJarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757
    Year of Publishing2020
    Electronic addresshttp://dx.doi.org/10.1515/ans-2018-2018
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