非线性三阶三点边值问题多个正解的存在性

Existence of Multiple Positive Solutions for NonlinearThird-Order Three-Point Boundary Value Problems

用锥上不动点定理研究非线性三阶三点边值问题u″′(t)-ρu′(t)+f(t,u(t))=0,t∈[0,1],u(0)=u′(0)=0,u′(1)=αu′(η)多个正解的存在性,其中ρ>0为一个常数,0<η<1,α>0,f:[0,1]×[0,∞)→[0,∞)是一个连续函数.结果表明:当f满足一定条件时,该问题存在可数多个正解.

By using the fixed point theorem in cones,the author study the existence of multiple positive solutions for nonlinear third-order three-point boundary value problems u(t)-ρu′(t)+f(t,u(t))=0,t∈[0,1],u(0)=u′(0)=0,u′(1)=αu′(η),whereρ>0 is a constant,0<η<1,α>0,f:[0,1]×[0,∞)→[0,∞)is a continuous function.The results show that when f satisfies certain conditions,there are countable multiple positive solutions for the problem.