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.

Badiale, M., Guida, M., Rolando, S. (2015). A nonexistence result for a nonlinear elliptic equation with singular and decaying potential. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 17(4) [10.1142/S0219199714500242].

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

#### Abstract

Several existence and nonexistence results are known for positive solutions [eqution presented] resting upon compatibility conditions between α and p. Letting 2α:= 2N/(N-α) and 2∗α:= 2(2N-2 + α)/(2N-2-α), the problem is still open for 0 < α < 2 and 2α < p ≤ 2∗α, for 2 < α < N and 2∗α ≥ p < 2α, and for N ≤ α < 2N-2 and p ≥ 2∗α. Here we give a negative answer to the problem of the existence of radial solutions in the first open case.
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Bessel functions; radial solution; Semilinear elliptic PDE; singular vanishing potential;
Semilinear elliptic PDE; singular vanishing potential; radial solution; Bessel functions
English
2015
Badiale, M., Guida, M., Rolando, S. (2015). A nonexistence result for a nonlinear elliptic equation with singular and decaying potential. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 17(4) [10.1142/S0219199714500242].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/106662`
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