%0 Journal Article
%T 一类非线性二阶常微分方程Dirichlet问题正解的存在性<br>Existence of Positive Solutions for a Class of Nonlinear Second-Order Dirichlet Problem
%A 叶芙梅
%J 四川大学学报 (自然科学版)
%D 2017
%X 本文研究了一类非线性二阶常微分方程~Dirichlet~边值问题 $$ \left\{\begin{array}{ll} u''-\ a(t)u+f(t,u)= 0,~~\ \ \ 0< t< 1\\[2ex] \ u(0)=\ u(1)=0 \end{array} \right.\eqno $$ 正解的存在性,~其中~$f: [0,1]\times R^{+}\rightarrow R^{+}$连续,~$a:[0,1]\rightarrow R^{+}$~连续.~主要结果的证明基于锥拉伸与压缩不动点定理.~<br>~In this paper,~ we study the existence of positive solutions for a class of nonlinear second-order Dirichlet problem ~ $$ \left\{\begin{array}{ll} u''-\ a(t)u+f(t,u)= 0,~~\ \ \ 0< t< 1\\[2ex] \ u(0)=\ u(1)=0 \end{array} \right.\eqno $$\~where~$f:[0,1]\times R^{+}\rightarrow R^{+}$~is continuous,~$a:[0,1]\rightarrow R^{+}$~is continuous.~The proof of the main results is based on the fixed-point theorem of cone expansion-compression
%K Dirichlet问题 锥 正解 存在性&lt
%K br&gt
%K Dirichlet problem cone positive solution existence
%U http://science.ijournals.cn/jsunature_cn/ch/reader/view_abstract.aspx?file_no=Z160561&flag=1