Coexistence of Unbounded Solutions and Periodic Solutions of a Class of Planar Systems with Asymmetric Nonlinearities
Liu, Qihuai ; Sun, Xiying ; Qian, Dingbian
Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, p. 577-591 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2010-08-15
Classification:  Successor map,  planar system,  unbounded solutions,  periodic solutions,  34C11,  34C25 
@article{1290608188,
     author = {Liu, Qihuai and Sun, Xiying and Qian, Dingbian},
     title = {Coexistence of Unbounded Solutions and Periodic Solutions of a Class of Planar Systems with Asymmetric Nonlinearities},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {17},
     number = {1},
     year = {2010},
     pages = { 577-591},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1290608188}
}

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, Tome 17 (2010) no. 1, pp.  577-591. http://gdmltest.u-ga.fr/item/1290608188/