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

Proceedings Mathematical Sciences

Huimin Yu²  L Haiyan¹  Yansheng Liu¹ 

[1] $$;Department of Mathematics, Shandong Normal University, Jinan 0 0, People’s Republic of China$$

关键词: Singular semipositone boundary value problem;    cone;    positive solution;    fixed point theorem.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 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)-𝜆 f(t,x)=0, & tin(0, 1);\ x(0)=x'(𝜂)=x"(1)=0,end{cases}end{equation*}where $frac{1}{2} < 𝜂 < 1$, the non-linear term $f(t,x): (0,1)×(0,=∞)→(-∞ +∞)$ is continuous and may be singular at 𝑡 = 0, 𝑡 = 1, and 𝑥 = 0, also may be negative for some values of 𝑡 and 𝑥, 𝜆 is a positive parameter.

【 授权许可】

Unknown