Positive and nodal solutions of the generalized BO-ZK equation

In this article, we establish the existence of a least-energy nodal solution and a positive ground state for nonlinear nonlocal problem involving the BO-ZK operator. By using constrained minimization on the Nehari-type manifolds, we prove the generalized BO-ZK equation has a least-energy nodal solution with its energy exceeding twice the least energy, and a positive ground state which both solutions are block-radial.