TY - JOUR
AU - Hakl, Robert
AU - Torres, Pedro J.
AU - Zamora, Manuel
PY - 2012/04/23
Y2 - 2022/01/22
TI - Periodic solutions to singular second order differential equations: the repulsive case
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 39
IS - 2
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2012.012
SP - 199 - 220
AB - This paper is devoted to study the existence of periodic solutions to the second-order differentialequation $u''+f(u)u'+g(u)=h(t,u)$, where $h$ is a Carathéodory function and $f,g$ are continuous functionson $(0,\infty)$ 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 tothe Rayleigh-Plesset equation, a physical model for the oscillations of a spherical bubble in a liquid underthe influence of a periodic acoustic field. Such a model has been the main motivation of this work.
ER -