Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 13, pp. 1-15.

Title: Existence of nontrivial solutions for Schrodinger-Kirchhoff equations 
 with indefinite potentials
       
Authors: Shuai Jiang (Xiamen Univ., Xiamen, China)
         Li-Feng Yin (Xiamen Univ., Xiamen, China)
         
Abstract:
We consider a class of Schrodinger-Kirchhoff equations in R<sup>3</sup>
with a general nonlinearity g and coercive sign-changing potential V so that
the Schrodinger operator -a&Delta; +V is indefinite. The nonlinearity considered
here satisfies the Ambrosetti-Rabinowitz type condition g(t)t&ge;&mu; G(t)&gt;0
with &mu;&gt;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.