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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Advanced Nonlinear Studies

ISSN

1536-1365

e-ISSN

—

Svazek periodika

19

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

16

Strana od-do

317-332

Kód UT WoS článku

000465562200004

EID výsledku v databázi Scopus

2-s2.0-85048113744