Nontrivial Solutions for 4-Superlinear Schrödinger–Kirchhoff Equations with Indefinite Potentials. (26th March 2021)

• Record Type: Journal Article
• Authors: Chen, Wei; Wu, Yue
• Other Names: Vetro Calogero Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-03-26
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/5551561
• Languages: English
• ISSNs: 2314-8896

Abstract

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.