Periodic solutions to singular second order differential equations: the repulsive case

0380708 - MÚ 2013 RIV PL eng J - Journal Article
Hakl, Robert - Torres, P.J. - Zamora, M.
Periodic solutions to singular second order differential equations: the repulsive case.
Topological Methods in Nonlinear Analysis. Roč. 39, č. 2 (2012), s. 199-220. ISSN 1230-3429. E-ISSN 1230-3429
Institutional support: RVO:67985840
Keywords : singular nonlinear boundary value problem * positive solutions * periodic solutions
Subject RIV: BA - General Mathematics
Impact factor: 1.099, year: 2012

This paper is devoted to study the existence of periodic solutions to the second-order differential equation u '' + f(u)u' + g(u) = h(t, u), where h is a Caratheodory function and f, g are continuous functions on (0, infinity) which may have singularities at zero. The repulsive case is considered. By using Schaefer's fixed point theorem, new conditions for existence of periodic solutions are obtained. Such conditions are compared with those existent in the related literature and applied to the Rayleigh-Plesset equation, a physical model for the oscillations of a spherical bubble in a liquid under the influence of a periodic acoustic field. Such a model has been the main motivation of this work.
Permanent Link: http://hdl.handle.net/11104/0211348