Multiple Positive Solutions to Third-Order Three-Point Singular Semipositone Boundary Value Problem

摘要

By using a specially constructed cone and the fixed point index theory, this paper investigates the existence of multiple positive solutions for the third-order three-point singular semipositone BVP:egin{equation*}egin{cases}x'"(t)-e??? f(t,x)=0, & tin(0, 1); x(0)=x'(e???)=x"(1)=0,end{cases}end{equation*}where $frac{1}{2} e??? 1$, the non-linear term $f(t,x): (0,1)?—(0,=a??)a?’(-a?? +a??)$ is continuous and may be singular at e?‘? = 0, e?‘? = 1, and e?‘￥ = 0, also may be negative for some values of e?‘? and e?‘￥, e??? is a positive parameter.