A new approach to solving a quasilinear boundary value problem with p-Laplacian using optimization

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...

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Bibliographic Details
Published in:Applications of mathematics (Prague) 2023-08, Vol.68 (4), p.425-439
Main Authors: Bailová, Michaela, Bouchala, Jiří
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Applications of Mathematics
Boundary value problems
Classical and Continuum Physics
Critical point
Existence theorems
Laplace transforms
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Optimization
Theoretical
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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.
ISSN:0862-7940
1572-9109
DOI:10.21136/AM.2023.0194-22