Sign-changing blowing-up solutions for the Brezis-Nirenberg problem in dimensions four and five
Articolo
Data di Pubblicazione:
2018
Citazione:
Sign-changing blowing-up solutions for the Brezis-Nirenberg problem in dimensions four and five / A. Iacopetti, G. Vaira. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - 18:1(2018), pp. 1-38. [10.2422/2036-2145.201602_003]
Abstract:
We consider the Brezis-Nirenberg problem
-Delta u = lambda u + vertical bar u vertical bar(p-1) u in Omega, u = 0 on partial derivative Omega,
where Omega is a smooth bounded domain in R-N, N >= 3, p = N+2/N-2 and lambda > 0.
We prove that, if Omega is symmetric and N = 4, 5, there exists a sign-changing solution whose positive part concentrates and blowsup at the center of symmetry of the domain, while the negative part vanishes, as lambda -> lambda(1), where lambda(1) = lambda(1)( Omega) denotes the first eigenvalue of -Delta on Omega, with zero Dirichlet boundary condition.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
critical sobolev exponents; nonlinear elliptc problems; nodal solutions; critical growth; asymptotic analysis; equations; existence; bifurcation; symmetry; domains
Elenco autori:
A. Iacopetti, G. Vaira
Link alla scheda completa: