Nonlocal discrete problem involving the anisotropic p(k)-capillarity differential operator

Stanislas Ouaro; Ismaël Nyanquini; Brahim Moussa

doi:10.56947/amcs.v28.522

Authors

Stanislas Ouaro Laboratoire de Mathématiques et d'Informatique, UFR/SEA, Université Nazi BONI, Burkina Faso
Ismaël Nyanquini Laboratoire de Mathématiques et d'Informatique, UFR/SEA, Université Nazi BONI, Burkina Faso.
Brahim Moussa Laboratoire de Mathématiques et d'Informatique, UFR/SEA, Université Joseph KI-ZERBO, Burkina Faso

DOI:

https://doi.org/10.56947/amcs.v28.522

Keywords:

Kirchhoff type equation, nonlocal discrete problem, p(k)-capillarity differential operator, boundary value problem, multiple solutions, mountain pass theorem, (S_ ) mapping theory.

Abstract

In this paper, we investigate the existence and multiplicity of solutions for a class of nonlocal discrete problems governed by a p(k)-capillarity differential operator in a T-dimensional Banach space. Our technical approach is based on a minimization method combined with adequate variational techniques, particularly the mountain pass theorem of A. Ambrosetti and P.H. Rabinowitz and the (S_+) mapping theory.