We deal with the following nonlinear problem involving fractional p&q Laplacians: (−∆)spu + (−∆)squ + |u|p−2u + |u|q−2u = λh(x)f(u) + |u|qs∗−2u in RN, where s ∈ (0, 1), 1 < p < q < Ns , qs∗ = NNq−sq, λ > 0 is a parameter, h is a nontrivial bounded perturbation and f is a superlinear continuous function with subcritical growth. Using suitable variational arguments and concentration-compactness lemma, we prove the existence of a nontrivial non-negative solution for λ sufficiently large.

Fractional p&q Laplacian problems in RN with critical growth / Ambrosio, V.. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - 39:3(2020), pp. 289-314. [10.4171/ZAA/1661]

Fractional p&q Laplacian problems in RN with critical growth

Ambrosio V.
2020-01-01

Abstract

We deal with the following nonlinear problem involving fractional p&q Laplacians: (−∆)spu + (−∆)squ + |u|p−2u + |u|q−2u = λh(x)f(u) + |u|qs∗−2u in RN, where s ∈ (0, 1), 1 < p < q < Ns , qs∗ = NNq−sq, λ > 0 is a parameter, h is a nontrivial bounded perturbation and f is a superlinear continuous function with subcritical growth. Using suitable variational arguments and concentration-compactness lemma, we prove the existence of a nontrivial non-negative solution for λ sufficiently large.
2020
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/11566/284888
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 35
  • ???jsp.display-item.citation.isi??? 35
social impact