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 Z(N), namely for any p > 1 and alpha is an element of (0, N) Delta(2)u - Delta u + V(x)u = (Sigma(y)EZ(N), (y not equal x) |u(y)p/d(x, y)(N-alpha)) |u|(p-2)u, where Delta(2) is the biharmonic operator, Delta is the IL -Laplacian, V : Z(N) -> 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 +alpha)/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.