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- Title
Multi-parameter, impulsive effects and positive periodic solutions of first-order functional differential equations.
- Authors
Zhang, Xuemei; Feng, Meiqiang
- Abstract
The authors consider the existence of positive periodic solution for the impulsive functional differential equation $u'(t)=-a(t)g(u(h_{1}(t)))u(t)+\lambda b(t)f (t, u(h_{2}(t)), \int_{-\zeta}^{0}e(s)u(t+s)\, ds )$, $t\in\mathbf{R}$, $t\neq t_{k}$, $u(t_{k}^{+})-u(t_{k})=\mu I_{k}(t_{k},u(t_{k}))$, $k\in\mathbf{Z}$, where $\lambda>0 $ and $\mu>0$ are two parameters. Several new and more general existence and multiplicity results are derived in terms of different values of $\lambda>0$ and $\mu>0$. Here we not only consider the case that g is bounded, but the case that g is not necessarily bounded is also considered. Our results improve those in (Ma et al. in J. Math. Anal. Appl. 384:527-535, 2011; Li et al. in Comput. Math. Appl. 56:2556-2560, 2008). Moreover, the parameter dependence of the periodic solution is also studied.
- Subjects
PARAMETERS (Statistics); NUMERICAL solutions to functional differential equations; EXISTENCE theorems; IMPULSIVE differential equations; MATHEMATICAL bounds
- Publication
Boundary Value Problems, 2015, Vol 2015, p1
- ISSN
1687-2762
- Publication type
Article
- DOI
10.1186/s13661-015-0401-x