On Existence of Multiple Normalized Solutions to a Class of Elliptic Problems in Whole $\mathbb{R}^N$ via Lusternik-Schnirelmann Category

Source abstract

Abstract. In this paper we study the existence of multiple normalized solutions to the class of elliptic problems [Formula: see text] where [Formula: see text], [Formula: see text] is an unknown parameter that appears as a Lagrange multiplier, [Formula: see text] is a continuous function, and [Formula: see text] is a differentiable function with [Formula: see text]-subcritical growth. It is proved that the numbers of normalized solutions are related to the topology of the set where the potential [Formula: see text] attains its minimum value. In the proof our main result, we apply minimization techniques and the Lusternik–Schnirelmann category.