吉林大学学报（理学版）2025，Vol.63Issue(3)：665-674,10.DOI:10.13413/j.cnki.jdxblxb.2024267
三点边值问题有限差分格式数值正解的存在性
Existence of Numerical Positive Solutions of Finite Difference Scheme for Three-Point Boundary Value Problems
摘要
Abstract
By using the critical point theory,we prove the existence of the non-trivial solution of the finite difference scheme{-Δ2u(k-1)=fk(u(k)),k ∈[1,n]z,{u(0)=αu(η),u(n+1)=0 for the three-point boundary value problem{-u"(x)=f(x,u(x)),x ∈[a,b],{u(a)=αu(η),u(b)=0,and get the existence result of the numerical correlation solution for the above continuous problem,where n≥3 is a positive integer,α,η are constants,and α(1-η/n+1)≠1,fk:R→R is continuous for any k ∈[1,n]z.关键词
临界点理论/先验界/Green函数/收敛/数值解Key words
critical point theorem/a priori bounded/Green function/convergence/numerical solution分类
数学引用本文复制引用
漆调艳,路艳琼..三点边值问题有限差分格式数值正解的存在性[J].吉林大学学报（理学版）,2025,63(3):665-674,10.基金项目
国家自然科学基金地区基金(批准号:12361040)和甘肃省青年科技基金计划项目(批准号:24JRRA536). （批准号:12361040）
