摘要
文中探讨了一类四阶非线性微分方程边值问题,并在一定条件下,利用上下解方法及不动点定理,得出此类问题解存在的充分条件.通过构造法将该边值问题转化为等价的积分方程,进而通过映射将积分方程转化为算子方程,并利用不动点定理证明了解的存在性.
This paper discusses a class of fourth order nonlinear differential equation boundary value problem, and under certain conditions, the use of upper and lower solutions method and fixed point theorem, concluded that sufficient conditions of existence for the solution of such problems. By constructing method, the boundary value problem is converted into the equivalent equation is converted into the operator equation, and the point theorem. integral equation, then by mapping the integral existence of solution is proved by using the fixed
出处
《通化师范学院学报》
2013年第8期10-12,共3页
Journal of Tonghua Normal University
关键词
四阶微分方程
边值问题
上下解方法
存在性
fourth -order differential equation
boundary value problem
upper and lower solutions method
existence
