非线性项含导数项的奇异半正脉冲微分方程多解的存在性  

Existence of Multiple Positive Solutions for Singular Semipositone Boundary Value Problem of Impulsive Differential Equations with the First Derivative in the Nonlinear Term

作　　者：黄明明[1] 路慧芹[1] 

机构地区：[1]山东师范大学数学科学学院,济南250014

出　　处：《应用泛函分析学报》2012年第3期298-305,共8页Acta Analysis Functionalis Applicata

基　　金：山东省高等学校科技计划项目(J09LA08)

摘　　要：利用不动点指数定理,讨论了脉冲微分方程边值问题正解的存在性,得到了一个正解存在的四个充分条件,以及至少两个正解存在的两个充分条件.这里的非线性项f变号,可能在t=0,t=1有奇性,并且含一阶导数.最后给出例子说明其应用.By using the fixed point index theory, this paper investigates the existence of positive solutions for boundary value problems of impulsive differential equations and gets four sufficient conditions about one positive solution and two sufficient conditions of two positive solutions. The nonlinear term can change the sign, may be singular at t = 0 and t -=1 and the first derivative is also in the nonlinear term. Finally, one example is provided to demonstrate the apptiation of the main results.

关 键 词：奇异性 正解 脉冲微分方程 不动点指数 

分 类 号：O175.8[理学—数学]