Electron. J. Differential Equations, Vol. 2023 (2023), No. 13, pp. 1-15.

Existence of nontrivial solutions for Schrodinger-Kirchhoff equations with indefinite potentials

Shuai Jiang, Li-Feng Yin

Abstract:
We consider a class of Schrodinger-Kirchhoff equations in R3 with a general nonlinearity g and coercive sign-changing potential V so that the Schrodinger operator -aΔ +V is indefinite. The nonlinearity considered here satisfies the Ambrosetti-Rabinowitz type condition g(t)t≥μ G(t)>0 with μ>3. We obtain the existence of nontrivial solutions for this problem via Morse theory.

Submitted March 28, 2022. Published February 10, 2023.
Math Subject Classifications: 35B38, 35J20, 35J60.
Key Words: Schrodinger-Kirchhoff equations; Palais-Smale condition; Morse theory.
DOI: https://doi.org/10.58997/ejde.2023.13

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Shuai Jiang
School of Mathematical Sciences
Xiamen University
Xiamen 361005, China
email: jiangshuai0915@163.com
Li-Feng Yin
School of Mathematical Sciences
Xiamen University
Xiamen 361005, China
email: yin136823@163.com

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