Nontrivial solutions for 4-superlinear Schrödinger-Kirchhoff equations with indefinite potentials (Q2025824)

Summary: This paper is devoted to the 4-superlinear Schrödinger-Kirchhoff equation \[-(a+b \int_{\mathbb{R}^3} |\nabla u|^2 \text{d}x)\Delta u+V(x) u=f (x,u),\quad\text{in }\mathbb{R}^3,\] where \(a>0\), \(b\geq 0\). The potential \(V\) here is indefinite so that the Schrödinger operator \(-\Delta+V\) possesses a finite-dimensional negative space. By using the Morse theory, we obtain nontrivial solutions for this problem.