A nonexistence result for sign-changing solutions of the Brezis-Nirenberg problem in low dimensions
Articolo
Data di Pubblicazione:
2015
Citazione:
A nonexistence result for sign-changing solutions of the Brezis-Nirenberg problem in low dimensions / A. Iacopetti, F. Pacella. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 258:12(2015 Jun), pp. 4180-4208. [10.1016/j.jde.2015.01.030]
Abstract:
We consider the Brezis-Nirenberg problem:
−∆u = λu + |u|^{2^*-2}u in Ω
u = 0 on partial Ω
where Ω is a smooth bounded domain in R^N , N ≥ 3, 2^∗ = 2N/(N-2) is the critical Sobolev exponent
and λ > 0 a positive parameter. The main result of the paper shows that if N = 4,5,6 and λ is close to zero there are no sign-changing solutions of the form u_λ =PU_{δ_1,ξ} −PU_{δ_2,ξ} +w_λ, where PU_{δ_i} is the projection on H_0^1(Ω) of the regular positive solution of the critical problem in R^N , centered at a point ξ ∈ Ω and w_λ is a remainder term.
Some additional results on norm estimates of w_λ and about the concentrations speeds of tower of bubbles in higher dimensions are also presented.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Semilinear elliptic equations; Critical exponent; Sign-changing solutions; Asymptotic behavior
Elenco autori:
A. Iacopetti, F. Pacella
Link alla scheda completa: