Nontrivial Solutions for 4-Superlinear Schrödinger–Kirchhoff Equations with Indefinite Potentials - Wei Chen; Yue Wu (Journal of Function Spaces)
This paper is devoted to the 4-superlinear Schrödinger–Kirchhoff equation −a+b∫ℝ3∇u2dxΔu+Vxu=fx,u,in ℝ3, 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.