具有不定位势Kirchhoff型Schrödinger-Bopp-Podolsky系统解的存在性

Existence of solutions for the Kirchhoff type Schrödinger-Bopp-Podolsky system with indefinite potentials

研究Kirchhoff型Schrödinger-Bopp-Podolsky系统,考虑位势函数V不定的情况。此时Schrödinger算子-△+V具有有限维负空间。利用Morse理论,得到Kirchhoff型Schrödinger-Bopp-Podolsky系统非平凡解的存在性。

This paper is devoted to the Kirchhoff type Schrödinger-Bopp-Podolsky system.It considers the case where the potential Vis indefinite so that the Schrödinger operator-A+V possesses a finite-dimensional negative space.The authors obtain nontrivial solutions for the Kirchhoff type Schrödinger-Bopp-Podolsky system via Morse theory.