In this paper we deal with the following fractional Kirchhoff problem [M(Rn×Rn|u(x)-u(y)|p|x-y|n+spdxdyp-1(-Δ)psu=f(x,u)+λ|u|r-2u in ω,u=0 in Rnω. Here ω ω ⊂ n is a smooth bounded open set with continuous boundary δω, p &insin; (1, +∞), s &insin; (0, 1), n > sp, (-Δ)ps is the fractional p-Laplacian, M is a Kirchhoff function, f is a continuous function with subcritical growth, λ is a nonnegative parameter and r > p*s where ps*-=np/n-sp is the fractional critical Sobolev exponent. By combining variational techniques and a truncation argument, we prove two existence results for this problem, provided that the parameter λ is sufficiently small.

Supercritical fractional Kirchhoff type problems / Ambrosio, V.; Servadei, R.. - In: FRACTIONAL CALCULUS & APPLIED ANALYSIS. - ISSN 1311-0454. - 22:5(2019), pp. 1351-1377. [10.1515/fca-2019-0071]

Supercritical fractional Kirchhoff type problems

Ambrosio V.;
2019-01-01

Abstract

In this paper we deal with the following fractional Kirchhoff problem [M(Rn×Rn|u(x)-u(y)|p|x-y|n+spdxdyp-1(-Δ)psu=f(x,u)+λ|u|r-2u in ω,u=0 in Rnω. Here ω ω ⊂ n is a smooth bounded open set with continuous boundary δω, p &insin; (1, +∞), s &insin; (0, 1), n > sp, (-Δ)ps is the fractional p-Laplacian, M is a Kirchhoff function, f is a continuous function with subcritical growth, λ is a nonnegative parameter and r > p*s where ps*-=np/n-sp is the fractional critical Sobolev exponent. By combining variational techniques and a truncation argument, we prove two existence results for this problem, provided that the parameter λ is sufficiently small.
2019
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/11566/278516
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 10
social impact