Ground states of a Kirchhoff equation with the potential on the lattice graphs.

In this paper, we study the nonlinear Kirchhoff equation − (a + b ∫ Z 3 | ∇ u | 2 d μ) Δ u + V (x) u = f (u) on lattice graph Z 3 , where a , b > 0 are constants and V : Z 3 → R is a positive function. Under a Nehari-type condition and 4-superlinearity condition on f , we use the Nehari method to prove the existence of ground-state solutions to the above equation when V is coercive. Moreover, we extend the result to noncompact cases in which V is a periodic function or a bounded potential well. In this paper, we study the nonlinear Kirchhoff equation on lattice graph , where are constants and is a positive function. Under a Nehari-type condition and 4-superlinearity condition on , we use the Nehari method to prove the existence of ground-state solutions to the above equation when is coercive. Moreover, we extend the result to noncompact cases in which is a periodic function or a bounded potential well. [ABSTRACT FROM AUTHOR]