## Differential and Integral Equations

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

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

Raúl F. Manásevich and Manuel A. del Pino

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1368397765

**Mathematical Reviews number (MathSciNet)**

MR1347988

**Zentralblatt MATH identifier**

0824.34040

**Subjects**

Primary: 34C25: Periodic solutions

Secondary: 34B15: Nonlinear boundary value problems 47H15 47N20: Applications to differential and integral equations

#### Citation

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