Differential and Integral Equations

$T$-periodic solutions for a second order system with singular nonlinearity

Abstract

We consider a system of the form \begin{align} & u''+au'=H_v(u,v)-h(t) \\ & v''+ bv'=H_u(u,v) - k(t), \end{align} where $h,k$ are locally integrable and $T$-periodic, and $H$ is a $C^1$ function defined on $(0,\infty)\times (0,\infty)$, for which a good model is given by $$H(u,v) = -( {1\over u^\alpha } + {1\over v^\beta } ),\quad \alpha ,\beta > 0 .$$ We state conditions under which existence of positive, $T$-periodic solutions for this system is ensured. We also study the problems of uniqueness and existence of multiple solutions in some special cases.

Article information

Source
Differential Integral Equations, Volume 8, Number 7 (1995), 1873-1883.

Dates
First available in Project Euclid: 12 May 2013

del Pino, Manuel A.; Manásevich, Raúl F. $T$-periodic solutions for a second order system with singular nonlinearity. Differential Integral Equations 8 (1995), no. 7, 1873--1883. https://projecteuclid.org/euclid.die/1368397765