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On Uniqueness of Solutions to the Boundary Value Problems on the Sierpiński Gasket
Numerical Functional Analysis and Optimization ( IF 1.2 ) Pub Date : 2021-05-28 , DOI: 10.1080/01630563.2021.1931310
Robert Stegliński 1
Affiliation  

Abstract

Using the monotonicity methods, we obtain conditions for the existence of the unique weak solution of Dirichlet problem

{Δu(x)+a(x)u(x)=f(x,u(x))xV\V0u|V0=0,

considered on the Sierpiński gasket. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are also given. We also consider a problem with parameters and we prove the theorem about continuous dependence on parameters.



中文翻译:

谢尔宾斯基垫片边值问题解的唯一性

摘要

使用单调性方法,我们获得了狄利克雷问题唯一弱解存在的条件

{Δ(X)+一种(X)(X)=F(X,(X))X\0|0=0,

考虑在谢尔宾斯基垫片上。我们主张某些假设的最优性。还给出了一些李雅普诺夫型不等式。我们还考虑了一个参数问题,并证明了关于参数连续依赖的定理。

更新日期:2021-06-29
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