Multiplicity of solutions for resonant discrete $2n$-th order periodic boundary value problem

O. Hammouti^a, N. Makran^b, S. Taarabti<sup>c

a</sup> Laboratory LAMA, Department of Mathematics, Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Mahraz, B.P 1796, Atlas Fez, Morocco
^b Department of Mathematical Sciences, Mohammed Premier University, Oujda, Morocco
^c LISTI, National School of Applied Sciences of Agadir, Ibn Zohr University, Agadir, Morocco

Abstract: We examine a class periodic boundary value problems for a discrete equation of order $2n$. We demonstrate the existence of multiple solutions by using the critical point theory and variational methods. Additionally, we consider two examples, in which we discuss the fundamental characteristics of the multiplicity of solutions.

Keywords: Discrete boundary value problems, equation of $2n$-th order, variational methods, critical point theory.

MSC: 39A10, 34B08, 34B15

Received: 08.08.2024

Language: English

 English version: Ufa Mathematical Journal, 2025, 17:3, 109–120