Periodic solutions to second-order indefinite singular equations

0474090 - MÚ 2018 RIV US eng J - Journal Article
Hakl, Robert - Zamora, M.
Periodic solutions to second-order indefinite singular equations.
Journal of Differential Equations. Roč. 263, č. 1 (2017), s. 451-469. ISSN 0022-0396. E-ISSN 1090-2732
Institutional support: RVO:67985840
Keywords : degree theory * indefinite singularity * periodic solution * singular differential equation
OECD category: Pure mathematics
Impact factor: 1.782, year: 2017
http://www.sciencedirect.com/science/article/pii/S0022039617301134

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.
Permanent Link: http://hdl.handle.net/11104/0271207