一类非线性四阶常微分方程边值问题正解的存在性

Existence of positive solutions for a class of nonlinear fourth-order ordinary differential equations with boundary values

本文研究了一类非线性四阶常微分方程边值问题{u^(4)(t)=λf(t,u(t)),t∈(0,1),u(0)=u″(0)=u(1)=0,u′(1)+C(u(1))u(1)=0正解的存在性,其中λ是一个正参数,f:[0,1]×R→[0,∞)满足L 1-Caratheodory条件,C:[0,∞)→[0,∞)连续.主要结果的证明基于锥拉伸与压缩不动点定理.

In this paper,we study the existence of positive solutions for a class of nonlinear fourth-order ordinary differential equations with boundary values:{u^(4)(t)=λf(t,u(t)),t∈(0,1),u(0)=u″(0)=u(1)=0,u′(1)+C(u(1))u(1)=0,whereλis a positive parameter,f:[0,1]×R→[0,∞)satisfies L 1-Caratheodory conditions,C:[0,∞)→[0,∞)is continuous.The proof of the main results is based on the fixed-point theorem of cone expansion-compression.