In this paper, we study the following problem {(−Δ)su=|u|2javax.xml.bind.JAXBElement@272dbf67javax.xml.bind.JAXBElement@56d2778c−2u+λu, in Ω,u=0, in RN∖Ω, where [Formula presented], [Formula presented], Ω is a bounded domain in RN, N>2s. We first show that if λ>0 is small, single bubbling solutions of (P) concentrating at a non-degenerate critical point of the Robin function is non-degenerate provided N≥4s+1. Then, using this result, we prove that if N∈[4s+1,6s] and Ω is a ball, (P) has infinitely many sign-changing bubbling solutions, whose energy can be arbitrarily large.
The fractional Brezis-Nirenberg problems on lower dimensions / Guo, Y.; Li, B.; Pistoia, A.; Yan, S.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 286:(2021), pp. 284-331. [10.1016/j.jde.2021.03.018]
The fractional Brezis-Nirenberg problems on lower dimensions
Pistoia A.
;
2021
Abstract
In this paper, we study the following problem {(−Δ)su=|u|2javax.xml.bind.JAXBElement@272dbf67javax.xml.bind.JAXBElement@56d2778c−2u+λu, in Ω,u=0, in RN∖Ω, where [Formula presented], [Formula presented], Ω is a bounded domain in RN, N>2s. We first show that if λ>0 is small, single bubbling solutions of (P) concentrating at a non-degenerate critical point of the Robin function is non-degenerate provided N≥4s+1. Then, using this result, we prove that if N∈[4s+1,6s] and Ω is a ball, (P) has infinitely many sign-changing bubbling solutions, whose energy can be arbitrarily large.| File | Dimensione | Formato | |
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