We are concerned with existence and multiplicity of nontrivial solutions for the Dirichlet problem Delta u + vertical bar u vertical bar(p-2)u = 0 in Omega, u = 0 on delta Omega, where Omega is a bounded domain of R-n, n >= 3, and p > 2n/n-2. We show that suitable perturbations of the domain, which modify its topological properties, give rise to a number of solutions which tends to infinity as the size of the perturbation tends to zero (some examples show that the perturbed domains may be even contractible). More precisely, we prove that for all k is an element of N, if the size of the perturbation is small enough (depending on k), there exist at least k pairs of nontrivial solutions, which concentrate near the perturbation as the size of the perturbation tends to zero. The method we use, which is completely variational, gives also further informations on the qualitative properties of the solutions; in particular. these solutions (which may change sign) do not have more than k nodal regions and at least two solutions (which minimize the corresponding energy functional) have constant sign.

Molle, R., Passaseo, D. (2006). Multiple solutions of supercritical elliptic problems in perturbed domains. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 23(3), 389-405 [10.1016/j.anihpc.2005.05.003].

Multiple solutions of supercritical elliptic problems in perturbed domains

MOLLE, RICCARDO;
2006-01-01

Abstract

We are concerned with existence and multiplicity of nontrivial solutions for the Dirichlet problem Delta u + vertical bar u vertical bar(p-2)u = 0 in Omega, u = 0 on delta Omega, where Omega is a bounded domain of R-n, n >= 3, and p > 2n/n-2. We show that suitable perturbations of the domain, which modify its topological properties, give rise to a number of solutions which tends to infinity as the size of the perturbation tends to zero (some examples show that the perturbed domains may be even contractible). More precisely, we prove that for all k is an element of N, if the size of the perturbation is small enough (depending on k), there exist at least k pairs of nontrivial solutions, which concentrate near the perturbation as the size of the perturbation tends to zero. The method we use, which is completely variational, gives also further informations on the qualitative properties of the solutions; in particular. these solutions (which may change sign) do not have more than k nodal regions and at least two solutions (which minimize the corresponding energy functional) have constant sign.
2006
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Changing sign solutions; Multiplicity of solutions; Number of nodal regions; Supercritical problems
Molle, R., Passaseo, D. (2006). Multiple solutions of supercritical elliptic problems in perturbed domains. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 23(3), 389-405 [10.1016/j.anihpc.2005.05.003].
Molle, R; Passaseo, D
Articolo su rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/38916
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 7
social impact