Article
| 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 |
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| Category: | math |
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| 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 |
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| Date available: | 2023-07-10T14:11:20Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151703 |
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