Volume 37 • Number 3 • 2014   • Asymptotic Behavior of Solutions of a Nonlinear Generalized Pantograph Equation with Impulses Kaizhong Guan and Qisheng Wang Abstract. Sufficient conditions are obtained on the asymptotic behavior of solutions of the nonlinear generalized pantograph equation with impulses \begin{equation}\begin{cases} x'(t)+p(t)f(x(\alpha t-\tau))=0, & t\geq t_{0}, \ t\neq t_{k},\\ x(t_{k})=b_{k}x(t^{-}_{k})+\frac{1-b_{k}}{\alpha}\int_{\alpha t_{k}-\tau}^{t_{k}}p\left(\frac{s+\tau}{\alpha}\right)f(x(s))ds, & k=1,2,.... \end{cases} \end{equation} 2010 Mathematics Subject Classification: 34K25, 34K45 Full text: PDF