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

Several existence and nonexistence results are known for positive solutions [eqution presented] resting upon compatibility conditions between α and p. Letting 2<inf>α</inf>:= 2N/(N-α) and 2∗<inf>α</inf>:= 2(2N-2 + α)/(2N-2-α), the problem is still open for 0 < α < 2 and 2<inf>α</inf> < p ≤ 2∗<inf>α</inf>, for 2 < <inf>α</inf> < N and 2∗<inf>α</inf> ≥ p < 2<inf>α</inf>, and for N ≤ α < 2N-2 and p ≥ 2∗<inf>α</inf>. Here we give a negative answer to the problem of the existence of radial solutions in the first open case.