A Novel Application of the Classical Banach Fixed Point Theorem

被引：0
作者：
Choudhuri D. [1 ]
机构：
[1] Department of Mathematics, National Institute of Technology Rourkela, Rourkela
来源：
International Journal of Applied and Computational Mathematics | 2017年 / 3卷 / 3期
关键词：
Contraction map; Elliptic PDE; Fixed point; Fundamental solution; Sobolev space;
D O I：
10.1007/s40819-016-0194-3
中图分类号：
学科分类号：
摘要：
Using the classical Banach fixed point theorem, we propose a novel method to obtain existence and uniqueness result pertaining to the solutions of semilinear elliptic partial differential equation of the type Δ u+ f(x, u, Du) = 0 , in Ω ⊂ R n and u| ∂ Ω = 0 , in a suitable Sobolev space. Here f:Ω×R×Rn→R is either a linear or a non-linear Lipshitz continuous function. The approach attempted here can be used as an algorithm by the numerical analysts to determine a solution to a partial differential equation of the above type. © 2016, Springer India Pvt. Ltd.
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页码：1799 / 1808
页数：9
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