Accepted for publication in JNEEA: Ms #2308241

Weak nontrivial solutions for discrete nonlinear problems of Kirchhoff type with variable exponents in a two dimensional Hilbert space

Idrissa IBRANGO, Dramane OUEDRAOGO, Aboudramane GUIRO

Laboratoire LaMIA, Université Nazi Boni, Bobo-Dioulasso, Burkina Faso

Received on August 24, 2023, revised October 28, 2023,
Accepted on December 10, 2023

Communicated by Mahamadi Warma

Abstract.  In this paper, we deal with the existence results for weak solutions to some problems of Kirchhoff type. The originality of this work lies in the generalization of discrete nonlinear problem of Kirchhoff type in a two dimensional Hilbert space with variable exponents. The proof is mainly based on the critical point theory. We then show that the energy functional associated to our problem is weakly lower semi-continuous, coercive and bounded from below.
Keywords: Discrete Kirchhoff type problem; Dirichlet boundary; critical point theory; weak solution; Hilbert space.
2010 Mathematics Subject Classification:   93A10, 35B38, 35P30, 34L05.

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