一类完全三阶边值问题解的存在性  

Existence of Solutions for a Class of FullyThird-Order Boundary Value Problem

作　　者：孙晓召 李永祥 SUN Xiaozhao;LI Yongxiang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《吉林大学学报（理学版）》2021年第1期13-19,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11661071).

摘　　要：用新的截断函数技巧与上下解方法,讨论完全三阶边值问题:u(t)=f(t,u(t),u′(t),u″(t)),t∈[0,1],u(0)=u′(1)=u″(1)=0解的存在性,其中f:[0,1]×ℝ3→ℝ连续.在非线性项f满足一些不等式的条件下给出该问题解的存在性.特别地,在不要求非线性项f非负的一般情形下得到了该问题正解的存在性.Using the new truncation function technique and the met hod of upper and lower solutions,we discussed the existence of solutions for the fully third-order boundary value problem:u(t)=f(t,u(t),u′(t),u″(t)),t∈[0,1],u(0)=u′(1)=u″(1)=0,where f:[0,1]×ℝ3→ℝwas a continuous function.Under the condition that the nonlinear term f satisfied some inequaliti es,we gave the existence of solutions to the problem.In particular,we obtained the existence o f the positive solutions to the problem when the nonlinear term f was not required to be non-negative.

关 键 词：完全三阶边值问题 存在性 上解 下解 正解 

分 类 号：O175.15[理学—基础数学]