Multi-bump Solutions for a Choquard Equation with Nonsymmetric Potential

In this paper, we study a class of Choquard equation with nonsymmetric potentials: \(\begin{aligned} -\Delta u+ (1+\delta V(x))u =\big (|x|^{-1}*|u|^{2}\big )u\hspace{4.14mm}\text{ in }\hspace{1.14mm} \mathbb {R}^3, \end{aligned}\) $$\begin{array}{c}\hfill -\mathrm{\Delta }u+(1+\delta V(x))u={(|x|}^{-1}\ast {|u|}^2)u\text{in}{\mathbb{R}}^3,\end{array}$$ where V is a continuous potential and satisfies some nondegeneracy condition. By using localized energy method, we prove that there exists \(\delta _0>0\) ${\delta }_0>0$ such that for \(0<\delta <\delta _0\) $0<\delta <{\delta }_0$ , the Choquard equation has infinitely many solutions with multi-bumps.