Validated numerical solutions for a semilinear elliptic equation on some topological annuli in the plane

被引：1

作者：

Arioli, Gianni ^{[1
]}

Koch, Hans ^{[2
]}

机构：

[1] Politecn Milan, Dept Math, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy

[2] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 353卷

关键词：

POSITIVE SOLUTIONS; EXISTENCE; VISUALIZATION; ALGORITHMS; SYSTEMS;

D O I：

10.1016/j.jde.2023.02.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the equation -Aw = w3 with zero boundary conditions on planar domains that are con-formal images of annuli. Starting with an approximate solution, we prove that there exists a true solution nearby. Our approach is computer-assisted. It involves simultaneous and accurate control of the (inverse) Dirichlet Laplacean, nonlinearities, and conformal mappings.(c) 2023 Elsevier Inc. All rights reserved.

引用

页码：420 / 436

页数：17

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