Existence and multiplicity of periodic solutions to indefinite singular equations having a non-monotone term with two singularities

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00504396" target="_blank" >RIV/67985840:_____/19:00504396 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1515/ans-2018-2018" target="_blank" >http://dx.doi.org/10.1515/ans-2018-2018</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/ans-2018-2018" target="_blank" >10.1515/ans-2018-2018</a>

Result language
angličtina
Original language name
Existence and multiplicity of periodic solutions to indefinite singular equations having a non-monotone term with two singularities
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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