Positive Green’s function and triple positive solutions of a second-order impulsive differential equation with integral boundary conditions and a delayed argument

被引：0
作者：
Gaoli Lu
Meiqiang Feng
机构：
[1] Beijing Information Science & Technology University,School of Applied Science
来源：
Boundary Value Problems | / 2016卷
关键词：
differential equations with impulsive effects and delayed arguments; positive Green’s function; three positive solutions; Legget-William’s fixed point theorem; Hölder’s inequality;
D O I：
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摘要：
In this paper, we first establish the expression of positive Green’s function for a second-order impulsive differential equation with integral boundary conditions and a delayed argument. Furthermore, applying Legget-William’s fixed point theorem and Hölder’s inequality, we obtain the existence results of at least three positive solutions under three cases: p=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p=1$\end{document}, 1<p<+∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1< p<+\infty$\end{document}, and p=+∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p=+\infty$\end{document}. We discuss our problem with impulsive effects and a delayed argument. In this case, our results cover second-order boundary value problems without impulsive effects and delayed arguments and are compared with some recent results. Finally, we give an example to illustrate our main results.
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共 45 条
[1]  
Yan J(2003)Existence and global attractivity of positive periodic solution for an impulsive Lasota-Wazewska model J. Math. Anal. Appl. 279 111-120
[2]  
Lalli BS(1994)On a periodic delay population model Q. Appl. Math. 52 35-42
[3]  
Zhang B(1990)Environmental periodicity and time delays in a food-limited population model J. Math. Anal. Appl. 147 545-555
[4]  
Gopalsamy K(2014)Transformation technique, fixed point theorem and positive solutions for second-order impulsive differential equations with deviating arguments Adv. Differ. Equ. 2014 593-610
[5]  
Kulenović MRS(2015)Deviating arguments, impulsive effects, and positive solutions for second order singular Adv. Differ. Equ. 2015 245-255
[6]  
Ladas G(2006)-Laplacian equations J. Math. Anal. Appl. 318 487-493
[7]  
Zhang X(1999)Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations Nonlinear Anal. 37 27-39
[8]  
Feng M(2010)Impulsive stabilization of functional differential equations by Lyapunov-Razumikhin functions Appl. Math. Lett. 23 435-452
[9]  
Zhang X(2015)New comparison results for impulsive functional differential equations J. Inequal. Appl. 2015 67-78
[10]  
Feng M(2009)Multi-parameter fourth order impulsive integral boundary value problems with one-dimensional J. Comput. Appl. Math. 223 491-507
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