一类非线性二阶常微分方程Dirichlet问题正解的存在性

本文研究了一类非线性二阶常微分方程Dirichlet边值问题{u″-a(t)u+f(t,u)=0,0t1,u(0)=u(1)=0正解的存在性,其中f:[0,1]×[0,∞)→[0,∞)连续,a(t):[0,1]→[0,∞)连续,主要结果的证明基于锥拉伸与压缩不动点定理.

Existence of Positive Solutions for a Class of Nonlinear Second-Order Dirichlet Problem

~In this paper,~ we study the existence of positive solutions for a class of nonlinear second-order Dirichlet problem ~$$left{begin{array}{ll}u''- a(t)u+f(t,u)= 0,~~ 0< t< 1[2ex] u(0)= u(1)=0end{array}right.eqno$$~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-pointtheorem of cone expansion-compression.