Sharp weighted-norm inequalities for functions with compact support in RN∖{0}

In this paper we study a class of Caffarelli–Kohn–Nirenberg inequalities without restricting the pertinent parameters. In particular, we determine the values of the corresponding optimal constants and the functions that achieve them, i.e., minimizers of a suitable functional. By studying a corresponding Euler–Lagrange equation, we also determine infinitely many sign-changing solutions at higher energy levels in addition to the found ground-state solutions.