Application of a Variant of Mountain Pass Theorem in Modeling Real Phenomena

Irina Meghea ()
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Irina Meghea: Department of Mathematical Methods and Models, Faculty of Applied Sciences, University Politehnica of Bucharest, 313 Splaiul Independentei, 060042 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 19, 1-12

Abstract: Mountain Pass Theorem (MPT) is an important result in variational methods with multiple applications in partial differential equations involved in mathematical physics. Starting from a variant of MPT, a new result concerning the existence of the solution for certain mathematical physics problems involving p -Laplacian and p -pseudo-Laplacian has been obtained. Based on the main theorem, the existence, possibly the uniqueness, and characterization of solutions for models such as nonlinear elastic membrane, glacier sliding, and pseudo torsion problem have been obtained. The novelty of the work consists of the formulation of the central result under weaker conditions requested by the chosen variant of MPT, the proof of this statement, and its application in solving above mentioned problems. While the expressions of such Dirichlet and/or von Neumann problems were already completed, this proposed solving method suggests some specific numerical methods to construct the appropriate solution. A general goal of this paper is the extension of the applicative pallet of this way to construct the solutions encountered in modeling real processes developed within new emerging technologies.

Keywords: variational method; p -Laplacian; p -pseudo-Laplacian; modeling real phenomena; mountain pass theorem; nonlinear elastic membrane; pseudo torsion problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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