Periodic solutions of singular second order differential equations : upper and lower functions

0370679 - MÚ 2012 RIV GB eng J - Journal Article
Hakl, Robert - Torres, P.J. - Zamora, M.
Periodic solutions of singular second order differential equations : upper and lower functions.
Nonlinear Analysis: Theory, Methods & Applications. Roč. 74, č. 18 (2011), s. 7078-7093. ISSN 0362-546X. E-ISSN 1873-5215
Institutional research plan: CEZ:AV0Z10190503
Keywords : second-order differential equation * singularity at the phase variable * Rayleigh-Plesset equation
Subject RIV: BA - General Mathematics
Impact factor: 1.536, year: 2011
http://www.sciencedirect.com/science/article/pii/S0362546X11005049

In this paper, we continue the study of the periodic problem for the second-order 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. Both attractive and repulsive singularities are considered. The method relies on a novel technique of construction of lower and upper functions. As an application, we obtain new sufficient conditions for the existence of periodic solutions to the Rayleigh-Plesset equation.
Permanent Link: http://hdl.handle.net/11104/0204404