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.
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页码：420 / 436
页数：17
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