The Ground State Solutions to a Class of Biharmonic Choquard Equations on Weighted Lattice Graphs

In this paper, we consider the biharmonic Choquard equation with the nonlocal term on the weighted lattice graph ZN, namely for any p 1 and α ∈ (0, N) Δ²u − Δu + V(x)u = ( ∑y∈ZN, y≠x |u(y)|p/d(x, y)N−α) |u| p−2u, where Δ² is the biharmonic operator, Δ is the μ-Laplacian, V : ZN → R is a function, and d(x, y) is the distance between x and y. If the potential V satisfies certain assumptions, using the method of Nehari manifold, we prove that for any p (N +α)/N, there exists a ground state solution of the above-mentioned equation. Compared with the previous results, we adopt a new method to finding the ground state solution from mountain-pass solutions.