Concentration of solutions with prescribed mass for (p,q)-Laplacian equations with nonlocal reaction

In this paper, we consider the following [Formula: see text]-Laplacian equation with nonlocal reaction [Formula: see text] where [Formula: see text], [Formula: see text] [Formula: see text] with [Formula: see text] is usual [Formula: see text]-Laplace operator, [Formula: see text] is the Hardy–Littlewood–Sobolev lower critical exponent, [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is an unknown parameter that appears as a Lagrange multiplier. [Formula: see text] [Formula: see text] is a continuous bounded function, [Formula: see text] is a continuous function with [Formula: see text]-subcritical growth, [Formula: see text] For the autonomous case, we establish some properties of minimal energy and introduce the compactness lemma to prove the existence of normalized solutions to this problem. For the non-autonomous case, we show the numbers of normalized solutions are related to the topology of the set where the potential [Formula: see text] attains its minimum by applying minimization techniques and the Lusternik–Schnirelmann category.