POSITIVE SOLUTIONS FOR ELLIPTIC EQUATIONS RELATED TO THE CAFFARELLI–KOHN–NIRENBERG INEQUALITIES

Abstract

In this paper, we are concerned with the following elliptic problems which are related to the well-known Caffarelli–Kohn–Nirenberg inequalities: [Formula: see text] where a = b < 0, [Formula: see text], a ≤ d ≤ a + 1, a ≤ e ≤ a + 1, [Formula: see text], [Formula: see text], 2 < q < D, λ and η are real constants. We obtain positive solutions for problem (0.1). Moreover, we establish a corresponding Pohozaev identity for problem (0.1), from which, the nonexistence of positive solutions for problem (0.1) is obtained.