摘要
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]×R^(3)→R连续.通过建立极大值原理,在非线性项f(t,x,y,z)关于x,y,z满足单调性条件的情形下,运用上下解的单调迭代方法,获得了解的存在性结果.
The existence of solutions is discussed 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]×R^(3)→R is continuous.By establishing the maximum principle,when f(t,x,y,z)satisfies the monotonicity conditions on x,y,z,the existence of solutions is obtained for the problem via monotone iterative method of lower and upper solutions.
作者
李永祥
孙晓召
LI Yong-xiang;SUN Xiao-zhao(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)
出处
《西北师范大学学报（自然科学版）》
CAS
北大核心
2021年第2期1-4,共4页
Journal of Northwest Normal University(Natural Science)
基金
国家自然科学基金资助项目(11661071,12061062)。
关键词
完全三阶边值问题
极大值原理
存在性
上下解
单调迭代
fully third-order boundary value problem
maximum principle
existence
lower and upper solution
monotone iterative
