摘要
含一个参数的一阶微分方程边值问题是指:含有未知量及它的一阶导数的方程的定解条件不仅依赖于在区间端点的取值,而且依赖于方程中的参数.通常它用不动点定理或逐步逼近法来解决.文章利用上下解方法和单调迭代技术讨论了含有一个参数的微分问题极值解的存在性,通过构造单调序列使这个单调序列一致收敛于非线性方程的极值解.
The boundary value problem for first-order differential equations with a parameter refers to the finite solution condition of equation which includes unknown quantity and its first-order derivative that not only relies on interval value but also relies on the parameter of the equation, which is always settled by fixed point theory or successive approximation meth- od. This paper considers existence of extreme solutions to first-order differential equations with a parameter by the method of lower and upper solutions with monotone iterations,and monotonic sequence is uniformly converged to the extreme value solution of nonlinear equation after being constructed.
出处
《周口师范学院学报》
CAS
2008年第5期21-23,共3页
Journal of Zhoukou Normal University
关键词
上下解
单调序列
收敛
极小解与极大解
lower and upper solutions
monotone sequence, convergence, minimal and maximal solutions
