Nontrivial Solutions for 4-Superlinear Schrödinger–Kirchhoff Equations with Indefinite Potentials

This paper is devoted to the 4-superlinear Schrödinger–Kirchhoff equation − a + b ∫ ℝ 3 ∇ u 2 d x Δ u + V x u = f x , u , in   ℝ 3 , where a > 0 , b ≥ 0 . The potential V here is indefinite so that the Schrödinger operator − Δ + V possesses a finite-dimensional negative space. By using the Morse theory, we obtain nontrivial solutions for this problem.