Nontrivial solutions for the choquard equation with indefinite linear part and upper critical exponent
Nontrivial solutions for the choquard equation with indefinite linear part and upper critical exponent
This paper is dedicated to studying the Choquard equation \begin{document}$ \begin{equation*} \left\{ \begin{array}{ll} -\Delta u+V(x)u = (I_{\alpha}\ast|u|^{p})|u|^{p-2}u+g(u),\; \; \; \; \; x\in\mathbb{R}^{N},\\ u\in H^{1}(\mathbb{R}^{N}) ,\\ \end{array} \right. \end{equation*} $\end{document} where $ N\geq4 $, $ \alpha\in(0, N) $, $ V\in\mathcal{C}(\mathbb{R}^{N}, \mathbb{R}) $ is sign-changing and periodic, $ I_{\alpha} $ is the …