Banach压缩映像原理应用分析

Analysis on the applications of the Banach contraction mapping principle

分别从空间的选取、Lipschitz常数的限制及局部解的存在区间等方面,用Banach压缩映像原理证明一阶常微分方程初值问题解的存在唯一性.以期使初学者加深对Picard定理的理解和掌握,体会Banach压缩映像原理在微分方程解的定性理论中的灵活应用,并为常微分方程课程的教学提供参考.

From the aspects of the selection of spaces, the restriction of Lipschitz constants and the existence interval of local solutions and by Banach contraction mapping principle, proves the existence and uniqueness of solutions to art initial value problem of the first order ordinary differential equations. The aims of this paper are for beginners to deepen the understanding and mastering of the Picard theorem and experience the flexible applications of the Banach contraction mapping principle in the qualitative theory of differential equations. Meanwhile, provides some references for the teaching of ordinary differential equations.