On Choquard Problems in ℝN Influenced by the Negative Part of the Spectrum

This article focuses on studying the existence of solutions for the following indefinite Choquard equation in $\mathbb{R}^{N}$: where $N \geq 2$. Here, $\alpha$ is a positive constant satisfying $0<\alpha In this work, we establish the existence of nontrivial solutions by employing significant outcomes from spectral theory, along with a version of the linking theorem presented by \cite{MaiaMayra}, and the interaction between translated solutions of the problem at infinity. AMS 2020 subject classification: 35A15, 35J10, 35P05.