## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Coexistence of Unbounded Solutions and Periodic Solutions of a Class of Planar Systems with Asymmetric Nonlinearities

#### Abstract

In this paper we will prove the coexistence of unbounded solutions and periodic solutions for a class of planar systems with asymmetric nonlinearities \begin{eqnarray*}\label{abstract} \left \{ \begin{array}{lll} u'=v-\alpha u^{+}+\beta u^{-} \\ v'=-\mu u^{+}+\gamma u^{-}-g(u)+p(t), \end{array} \right. \end{eqnarray*} where $g(u)$ is continuous and bounded, $p(t)$ is a continuous $2\pi$-periodic function and $\alpha, \beta\in \mathbb{R}, \mu, \gamma$ are positive constants.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 17, Number 4 (2010), 577-591.

Dates
First available in Project Euclid: 24 November 2010

https://projecteuclid.org/euclid.bbms/1290608188

Mathematical Reviews number (MathSciNet)
MR2778438

Zentralblatt MATH identifier
1213.34062

Subjects
Primary: 34C11: Growth, boundedness 34C25: Periodic solutions

#### Citation

Liu, Qihuai; Sun, Xiying; Qian, Dingbian. Coexistence of Unbounded Solutions and Periodic Solutions of a Class of Planar Systems with Asymmetric Nonlinearities. Bull. Belg. Math. Soc. Simon Stevin 17 (2010), no. 4, 577--591. https://projecteuclid.org/euclid.bbms/1290608188