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Periodic solutions to second-order indefinite singular equations
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SYSNO ASEP 0474090 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Periodic solutions to second-order indefinite singular equations Author(s) Hakl, Robert (MU-W) RID, SAI, ORCID
Zamora, M. (CL)Source Title Journal of Differential Equations. - : Elsevier - ISSN 0022-0396
Roč. 263, č. 1 (2017), s. 451-469Number of pages 19 s. Language eng - English Country US - United States Keywords degree theory ; indefinite singularity ; periodic solution ; singular differential equation Subject RIV BA - General Mathematics OECD category Pure mathematics Institutional support MU-W - RVO:67985840 UT WOS 000400123300014 EID SCOPUS 85014590033 DOI 10.1016/j.jde.2017.02.044 Annotation The efficient conditions guaranteeing the existence of a T-periodic solution to the second order differential equation u...=h(t)g(u) are established in the paper. Here, g is a positive and decreasing function which has a strong singularity at the origin, and the weight h\in(R/TZ) is a sign-changing function. The obtained results have the form of relation between the multiplicities of the zeroes of the weight function h and the order of the singularity of the nonlinear term. The approach is based on Leray–Schauder degree theory, proving that no T-periodic solution of a certain homotopy appears on the boundary of an unbounded open set during the deformation to an autonomous problém. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2018
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