Multibump Solutions for Critical Choquard Equation

Abstract. We are concerned with the critical Choquard equation [Formula: see text] where [Formula: see text], [Formula: see text] is the Riesz potential with order [Formula: see text], and the exponent [Formula: see text] is critical with respect to the Hardy–Littlewood–Sobolev inequality. By combining the variational gluing method and a penalization technique, for every [Formula: see text], we prove the existence of infinitely many [Formula: see text]-bump positive solutions for this nonlocal equation exhibiting a polynomial decay at infinity if the potential [Formula: see text] is periodic in one of its variables and permits a global maxima with a fast decay rate near the maximum point. Our results demonstrate the nonlocal features of the Choquard equation and do not depend on the uniqueness or nondegeneracy property of positive solutions, which is in contrast to the results of the local Yamabe equation.