Ground state and sign-changing solutions for discrete fractional Kirchhoff–Schrödinger equations

This paper focuses on the existence of solutions for a class of discrete fractional nonlinear Schrödinger equations of Kirchhoff type on the one-dimensional integer lattice Z (a1+a2[u]s2)(−Δ1)su+V(m)u=f(m,u),∀ m∈Z, where a1,a2>0 and (−Δ1)s denotes the discrete fractional Laplacian of order s∈(0,1). First of all, we establish the existence of a ground state solution on the Nehari manifold N by employing the mountain pass theorem. Next, by utilizing the Poincaré-Miranda theorem in conjunction with the deformation lemma, we prove the existence of a least energy sign-changing solution on the nodal manifold M. Finally, we demonstrate that the least energy of the sign-changing solution is strictly greater than twice the ground state energy.