A nonexistence result for a nonlinear elliptic equation with singular and decaying potential

Abstract

Several existence and nonexistence results are known for positive solutions u ∈ D1,2(ℝN) ∩ L2(ℝN, ∣x∣-αdx) ∩ Lp(ℝN) to the equation [Formula: see text] resting upon compatibility conditions between α and p. Letting 2α := 2N/(N - α) and [Formula: see text], the problem is still open for 0 < α < 2 and [Formula: see text], for 2 < α < N and [Formula: see text], and for N ≤ α < 2N - 2 and [Formula: see text]. Here we give a negative answer to the problem of the existence of radial solutions in the first open case.