Banach空间半直线上非线性二阶微分方程组正解的存在性

Existence of Positive Solutions for Systems of Nonlinear Second-Order Differential Equations on the Half Line in a Banach Space

中文关键词:  奇异微分方程组  锥与半序  正解  M\"onch 不动点定理  非紧性测度.

英文关键词:systems of singular differential equations  cone and ordering  positive solutions  M\"onch fixed point theorem  measure of non-compactness.

中文摘要:

      利用锥理论和M\"onch不动点定理结合单调迭代技巧给出了Banach空间中半直线上奇异二阶微分方程组正解存在的充分条件,并给出解的迭代程序.

英文摘要:

      In this paper, the cone theory and M\"onch fixed point theorem combined with the monotone iterative technique are used to investigate the positive solutions for a class of systems of nonlinear singular differential equations with multi-point boundary value conditions on the half line in a Banach space. The conditions for the existence of positive solutions are formulated. In addition, an explicit iterative approximation of the solution is also derived.