Kirchhoff equations with indefinite potentials

Abstract

In this paper we consider four-superlinear Kirchhoff equations. In contrast to most studies, we allowed the potential V is indefinite, precisely, the operator $-\mathrm{\Delta }+V$ possesses a finite-dimensional negative space. When the working space loss compactness property, we obtain nontrivial solutions via Morse theory.

Keywords:

• Kirchhoff equations
• indefinite potential
• Morse theory

2010 Mathematics Subject Classifications:

• Primary: 35J60
• Secondary: 35J20
• 58E05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by Research Fund of National Natural Science Foundation of China [grant numbers 11601046, 11861046, 11601048], China Postdoctoral Science Foundation [grant numbers 2019M662796, 2019M652348], Chongqing Municipal Education Commission [grant numbers KJQN20190081, KJQN201900539].