含有所有阶导数的2n阶非线性常微分方程边值问题的正解  

Positive Solutions for a 2n-order Boundary Value Problem Involving Derivatives of all Lower Orders

作　　者：王晓梅 杨志林[1] WANG Xiao-mei;YANG Zhi-lin(Department of Mathematics,Qingdao University of Technology,Qingdao 266033,China)

机构地区：[1]青岛理工大学理学院,山东青岛266033

出　　处：《数学的实践与认识》2020年第15期229-237,共9页Mathematics in Practice and Theory

摘　　要：主要研究以下含有所有低阶导数的2n阶非线性常微分方程边值问题正解的存在性、多重正解的存在性和正解的唯一性:■其中f∈C([0,1]×R+2n,R+)(R+=[0,+∞]).借助于建立的积分恒等式和积分不等式,在先验估计的基础上,利用不动点指数理论证明了本文的主要结果.This article is mainly concerned with the existence,multiplicity and uniqueness of positive solutions for the 2 n-order boundary value problem■wheref∈C([0,1]×R+2n,R+).Based on a priori estimates achieved by utilizing some integral identities and integral inequalities,we use fixed point index theory to establish our main results.

关 键 词：2n阶边值问题 正解 先验估计法 不动点指数 

分 类 号：O175.8[理学—数学]