Data di Pubblicazione:
2015
Citazione:
Asymptotic analysis for radial sign-changing solutions of the Brezis-Nirenberg problem / A. Iacopetti. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 194:6(2015), pp. 1649-1682. [10.1007/s10231-014-0438-y]
Abstract:
We study the asymptotic behavior, as lambda -> 0, of least energy radial sign-changing solutions u(lambda), of the Brezis-Nirenberg problem
{-Delta u = lambda u + vertical bar u vertical bar(2*-2)u in B-1
u = 0 on partial derivative B-1,
where lambda > 0, 2* = 2n/n-2 and B-1 is the unit ball of R-n, n >= 7. We prove that both the positive and negative part u(lambda)(+) and u(lambda)(-) concentrate at the same point (which is the center) of the ball with different concentration speeds. Moreover, we show that suitable rescalings of u(lambda)(+) and u(lambda)(-) converge to the unique positive regular solution of the critical exponent problem in R-n. Precise estimates of the blow-up rate of vertical bar vertical bar u(lambda)(+/-)vertical bar vertical bar infinity are given, as well as asymptotic relations between vertical bar vertical bar u(lambda)(+/-)vertical bar vertical bar infinity and the nodal radius r(lambda). Finally, we prove that, up to constant, lambda -n-2/2n-8 u(lambda) converges in C-loc(1) (B-1 - {0}) to G(x, 0), where G(x, y) is the Green function of the Laplacian in the unit ball.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Semilinear elliptic equations; Critical exponent; Sign-changing radial solutions; Asymptotic behavior
Elenco autori:
A. Iacopetti
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