(untitled) (Journal of Partial Differential Equations, 2024)
We investigate the Kirchhoff type elliptic problem (a+b_R^N[| abla u|^2+V(x)u^2]dx)[-Δ u+V(x)u]=f(x,u), xR^N,where both V and f are periodic in x, 0 belongs to a spectral gap of −∆+V. Under suitable assumptions on V and f with more general conditions, we prove the existence of ground state solutions and infinitely many geometrically distinct solutions.