## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

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

Qihuai Liu, Dingbian Qian, and Xiying Sun

#### 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

**Permanent link to this document**

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

**Mathematical Reviews number (MathSciNet)**

MR2778438

**Zentralblatt MATH identifier**

1213.34062

**Subjects**

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

**Keywords**

Successor map planar system unbounded solutions 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