Weak solutions of a discrete Robin problem involving the anisotropic $\vect{p}$-mean curvature operator

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Résumé

This work investigates the existence and uniqueness of a so- lution to a discrete Robin boundary value problem involving the anisotropic p⃗-mean curvature operator. The existence re- sult is established through variational methods, specifically by applying the Mountain Pass Theorem of Ambrosetti and Rabinowitz in combination with Ekeland’s Variational Prin- ciple. Uniqueness is obtained under the assumption of Lips- chitz continuity on the nonlinear term

Mots-clés

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