Weak solutions of a discrete Robin problem involving the anisotropic \(\vec{p}\)-mean curvature operator

Brahim Moussa; Ismaël Nyanquini; Stanislas Ouaro

doi:10.56754/0719-0646.2801.001

DOI:

https://doi.org/10.56754/0719-0646.2801.001

Abstract

This work investigates the existence and uniqueness of a solution to a discrete Robin boundary value problem involving the anisotropic \(\vec{p}\)-mean curvature operator. The existence result is established through variational methods, specifically by applying the Mountain Pass Theorem of Ambrosetti and Rabinowitz in combination with Ekeland’s Variational Principle. Uniqueness is obtained under the assumption of Lipschitz continuity on the nonlinear term.

Keywords

Discrete Robin problem , boundary value problems , anisotropic p-mean curvature operator , critical point , nontrivial solution , mountain pass theorem , Ekeland variational principle

Mathematics Subject Classification:

47A75 , 35B38 , 35P30 , 34L05 , 34L30

Brahim Moussa Laboratoire de Mathématiques et Informatique, UFR/SEA, Université Nazi BONI, 01 BP 1091 Bobo-Dioulasso 01, Burkina Faso. https://orcid.org/0009-0000-5230-3220
Ismaël Nyanquini Laboratoire de Mathématiques et Informatique, UFR/SEA, Université Nazi BONI, 01 BP 1091 Bobo-Dioulasso 01, Burkina Faso. https://orcid.org/0009-0003-1342-0004
Stanislas Ouaro Laboratoire de Mathématiques et Informatique, UFR/SEA, Université Joseph KI-ZERBO, 03 BP 7021 Ouagadougou 03, Burkina Faso. https://orcid.org/0000-0003-0671-2378

Pages: 1-26
Date Published: 2026-01-13
Vol. 28 No. 1 (2026)

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