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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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    0504396 - MÚ 2020 RIV DE eng J - Journal Article
    Hakl, Robert - Zamora, M.
    Existence and multiplicity of periodic solutions to indefinite singular equations having a non-monotone term with two singularities.
    Advanced Nonlinear Studies. Roč. 19, č. 2 (2019), s. 317-332. ISSN 1536-1365
    Institutional support: RVO:67985840
    Keywords : indefinite weight * periodic solution * singular differential equation
    Subject RIV: BA - General Mathematics
    OBOR OECD: Applied mathematics
    Impact factor: 1.533, year: 2019
    http://dx.doi.org/10.1515/ans-2018-2018

    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.
    Permanent Link: http://hdl.handle.net/11104/0296036
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