| Title:
|
A new approach to solving a quasilinear boundary value problem with $p$-Laplacian using optimization (English) |
| Author:
|
Bailová, Michaela |
| Author:
|
Bouchala, Jiří |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
68 |
| Issue:
|
4 |
| Year:
|
2023 |
| Pages:
|
425-439 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a novel approach to solving a specific type of quasilinear boundary value problem with $p$-Laplacian that can be considered an alternative to the classic approach based on the mountain pass theorem. We introduce a new way of proving the existence of nontrivial weak solutions. We show that the nontrivial solutions of the problem are related to critical points of a certain functional different from the energy functional, and some solutions correspond to its minimum. This idea is new even for $p=2$. We present an algorithm based on the introduced theory and apply it to the given problem. The algorithm is illustrated by numerical experiments and compared with the classic approach. (English) |
| Keyword:
|
$p$-Laplacian operator |
| Keyword:
|
quasilinear elliptic PDE |
| Keyword:
|
critical point and value |
| Keyword:
|
optimization algorithm |
| Keyword:
|
gradient method |
| MSC:
|
35B38 |
| MSC:
|
35J92 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 07729505 |
| idMR:
|
MR4612741 |
| DOI:
|
10.21136/AM.2023.0194-22 |
| . |
| Date available:
|
2023-07-10T14:11:20Z |
| Last updated:
|
2025-09-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151703 |
| . |
| Reference:
|
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