Nontrivial Solutions for 4-Superlinear Schrödinger–Kirchhoff Equations with Indefinite Potentials. (26th March 2021) - Chen, Wei; Wu, Yue
Abstract : 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.