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Tang, L.Q., Wang, L., Wang, J., et al. (2023) Existence of Solutions for the Kirchhoff Type Schrödinger-Bopp-Podolsky System with Indefinite Potentials. Journal of Shandong University (Nature Science), 58, 97-103.

has been cited by the following article:

• TITLE: Existence of Solutions for the Schrödinger-Type Bopp-Podolsky System with Indefinite Potentials

  AUTHORS: Li Chen

  KEYWORDS: Schrödinger-Type Bopp-Podolsky System, Morse Theory, Critical Group, Indefinite Potential

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.1, December 31, 2025

  ABSTRACT: This paper investigates the existence of nontrivial solutions for the Schrödinger-Bopp-Podolsky system with an indefinite potential function V( x ) . The indefiniteness of V prevents the direct application of standard variational methods such as the mountain pass theorem, as the associated Schrödinger operator −Δ+V possesses a finite-dimensional negative space, leading to a loss of coercivity and the standard linking structure in the energy functional. By employing a reduction method to handle the coupling with the Bopp-Podolsky equation and applying Morse theory combined with critical groups at infinity, we establish the existence of at least one nontrivial solution under appropriate assumptions on the indefinite potential V . and the nonlinearity g .