Three Symmetric Positive Solutions for Second-order Nonlocal Boundary Value Problems  

作　　者：Yong-ping Sun 

机构地区：[1]College of Electron and Information, Zhejiang University of Media and Communications, Hangzhou 310018,China

出　　处：《Acta Mathematicae Applicatae Sinica》2011年第2期233-242,共10页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of Zhejiang Province of China(No.Y605144);the Science Research Foundation of Educational Department of Zhejiang Province of China(No.200804671)

摘　　要：Using the Leggett-Williams fixed point theorem, we will obtain at least three symmetric positive solutions to the second-order nonlocal boundary value problem of the form u″（t）＋g（t）f（t,u（t））=0,0〈t〈1,u（0）=u（1）=∫01m（s）u（s）ds. where m ∈ L1[0 1], g ： （0, 1）→ [0, ∞） is continuous, symmetric on （0, 1） and maybe singular at t = 0 and t = 1, f： [0, 1] × [0, ∞） → [0, ∞） is continuous and f（-, x） is symmetric on [0, 1] for all x∈ [0, ∞）.Using the Leggett-Williams fixed point theorem, we will obtain at least three symmetric positive solutions to the second-order nonlocal boundary value problem of the form u″（t）＋g（t）f（t,u（t））=0,0〈t〈1,u（0）=u（1）=∫01m（s）u（s）ds. where m ∈ L1[0 1], g ： （0, 1）→ [0, ∞） is continuous, symmetric on （0, 1） and maybe singular at t = 0 and t = 1, f： [0, 1] × [0, ∞） → [0, ∞） is continuous and f（-, x） is symmetric on [0, 1] for all x∈ [0, ∞）.

关 键 词：symmetric positive solution nonlocal boundary value problem fixed point theorem 

分 类 号：O175.25[理学—数学] O175.8[理学—基础数学]