On the Existence of One Positive Solution for the Logarithmic Schrödinger–Bopp–Podolsky System With Saddle‐Like Potential

ABSTRACT This paper deals with the logarithmic Schrödinger–Bopp–Podolsky system with a saddle‐like potential. By using a special minimax level and the variational method developed by Szulkin for functionals that are the sum of a smooth functional and a convex lower semicontinuous functional, we prove the existence of a positive solution when the parameters of the system are sufficiently small.