We discuss the existence and the asymptotic behavior of positive radial solutions for the following equation: Δpu(x) + f (u, x) = 0, where Δpu = div(Dup-2Du), x ℝn, n > p > 1, and we assume that f ≥ 0 is subcritical for u large and x small and supercritical for u small and x large, with respect to the Sobolev critical exponent. We give sufficient conditions for the existence of ground states with fast decay. As a corollary we also prove the existence of ground states with slow decay and of singular ground states with fast and slow decays. For the proofs we use a Fowler transformation which enables us to use dynamical arguments. This approach allows to unify the study of different types of non-linearities and to complete the results already appeared in literature with the analysis of singular solutions.

Fowler transformation and radial solutions for quasilinear elliptic equations. Part 2: nonlinearities of mixed type / Franca, Matteo. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 189:1(2010), pp. 67-94. [10.1007/s10231-009-0101-1]

Fowler transformation and radial solutions for quasilinear elliptic equations. Part 2: nonlinearities of mixed type.

FRANCA, Matteo
2010-01-01

Abstract

We discuss the existence and the asymptotic behavior of positive radial solutions for the following equation: Δpu(x) + f (u, x) = 0, where Δpu = div(Dup-2Du), x ℝn, n > p > 1, and we assume that f ≥ 0 is subcritical for u large and x small and supercritical for u small and x large, with respect to the Sobolev critical exponent. We give sufficient conditions for the existence of ground states with fast decay. As a corollary we also prove the existence of ground states with slow decay and of singular ground states with fast and slow decays. For the proofs we use a Fowler transformation which enables us to use dynamical arguments. This approach allows to unify the study of different types of non-linearities and to complete the results already appeared in literature with the analysis of singular solutions.
2010
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/11566/39376
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 13
  • ???jsp.display-item.citation.isi??? 13
social impact