Existence of periodic solutions for a class of $ (\phi_{1}, \phi_{2}) $-Laplacian discrete Hamiltonian systems

Abstract

In this paper, we consider the existence of periodic solutions for a class of nonlinear difference systems involving classical $ (\phi_{1}, \phi_{2}) $-Laplacian. By using the least action principle, we obtain that the system with classical $ (\phi_{1}, \phi_{2}) $-Laplacian has at least one periodic solution when potential function is $ (p, q) $-sublinear growth condition, subconvex condition. The results obtained generalize and extend some known works.

Keywords

• (ϕ1，ϕ2)-laplacian
• discrete systems
• periodic solutions
• the least action principle