We study the nodal solutions of the Lane-Emden-Dirichlet problem{-Δu=|u|p-1u,in Ω,u=0,on ∂Ω, where Ω is a smooth bounded domain in R2 and p>1. We consider solutions up satisfyingp∫Ω|up|2→16πeas p→+∞ and we are interested in the shape and the asymptotic behavior as p→+∞. First we prove that (*) holds for least energy nodal solutions. Then we obtain some estimates and the asymptotic profile of this kind of solutions. Finally, in some cases, we prove that pup can be characterized as the difference of two Greens functions and the nodal line intersects the boundary of Ω, for large p. © 2012 Elsevier Masson SAS. All rights reserved.
Lane-Emden problems: Asymptotic behavior of low energy nodal solutions / Grossi, Massimo; Grumiau, Christopher; Pacella, Filomena. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 30:1(2013), pp. 121-140. [10.1016/j.anihpc.2012.06.005]
Lane-Emden problems: Asymptotic behavior of low energy nodal solutions
GROSSI, Massimo;PACELLA, Filomena
2013
Abstract
We study the nodal solutions of the Lane-Emden-Dirichlet problem{-Δu=|u|p-1u,in Ω,u=0,on ∂Ω, where Ω is a smooth bounded domain in R2 and p>1. We consider solutions up satisfyingp∫Ω|up|2→16πeas p→+∞ and we are interested in the shape and the asymptotic behavior as p→+∞. First we prove that (*) holds for least energy nodal solutions. Then we obtain some estimates and the asymptotic profile of this kind of solutions. Finally, in some cases, we prove that pup can be characterized as the difference of two Greens functions and the nodal line intersects the boundary of Ω, for large p. © 2012 Elsevier Masson SAS. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
