Liouville type theorems for some fractional elliptic problems

Liouville type theorems for solutions of the weighted fractional Lane-Emden system

“…Our results generalize the results established in [23] for the Laplacian case (correspond to s = 1) and improve the previous work [13]. As a consequence, we prove classification result for stable solutions to the weighted fractional Lane-Emden equation (−∆) s u = h(x)u p in R N .…”

“…In [13], Duong-Nguyen studied a more general fractional equation, obtaining similar results of [15, Theorem 1.5] for the Laplacian case.…”

“…At last, using the Definition 1.1 of stability, we can derive the following estimate which is crucial for our analysis. Its proof comes from ideas in [6,16,4,13] and is very similar to the mentioned works, so we omit the details. Lemma 2.3.…”

“…For the non local Lane-Emden system (1.1), the first result (up to our knowledge) classifying stable solutions is proved in [13] for h = 1 and s ∈ (0, 1):…”

“…(2) If 1 < q ≤ min(p, 4 3 ), t − 0 < q 2 and (1.7), then (1.6) has no stable solution. In this paper, our aim is to generalize [23,13]. Our main results state as follows Theorem 1.2.…”