Positive solutions to (n-1,1) m-point boundary value problems with dependence on the first order derivative  

作　　者：纪玉德 郭彦平 禹长龙 

机构地区：[1]College of Sciences,Hebei University of Science and Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2009年第4期527-536,共10页应用数学和力学（英文版）

基　　金：supported by the Natural Science Foundation of Hebei Province of China (No. A2006000298);the Foundation of Hebei University of Science and Technology (No. XL2006040)

摘　　要：Using the extension of Krasnoselskii＇s fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green＇s function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results.Using the extension of Krasnoselskii＇s fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green＇s function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results.

关 键 词：Green＇s function fixed point theorem in a cone positive solution higher-order differential equation 

分 类 号：O175.8[理学—数学]