Positive solutions to nonlinear second-order three-point boundary-value problems for difference equation with change of sign

Electronic Journal of Differential Equations

关键词: Boundary value problem;    positive solution;    difference equation;    fixed point;    changing sign coefficients;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this paper we investigate the existence of positive solution tothediscrete second-order three-point boundary-value problem$$displaylines{Delta^2 x_{k-1}+ h(k) f(x_k)=0, quadk in [1, n], crx_0 =0,quada x_l = x_{n+1},}$$where$n in [2, infty)$, $l in [1, n]$, $0 < a < 1$,$(1-a)l geq 2$, $(1+a)lleq n+1$, $f in C(mathbb{R}^+,mathbb{R}^+)$ and $h(t)$ is a function that may change sign on $[1, n]$.Using the fixed-point index theory, we prove the existence ofpositive solution for the above boundary-value problem.

【 授权许可】

Unknown