In this paper, we deal with the following class of fractional (p, q)-Laplacian Kirchhoff type problem: {(1+[u]s,pp)(-Δ)psu+(1+[u]s,qq)(-Δ)qsu+V(εx)(|u|p-2u+|u|q-2u)=f(u)inRN,u∈Ws,p(RN)∩Ws,q(RN),u>0inRN,where ε> 0 , s∈ (0 , 1) , 1<2q, (-Δ)ts, with t∈ { p, q} , is the fractional t-Laplacian operator, V: RN→ R is a positive continuous potential such that inf ∂ΛV> inf ΛV for some bounded open set Λ ⊂ RN, and f: R→ R is a superlinear continuous nonlinearity with subcritical growth at infinity. By combining the method of Nehari manifold, a penalization technique, and the Lusternik–Schnirelman category theory, we study the multiplicity and concentration properties of solutions for the above problem when ε→ 0.

A Kirchhoff Type Equation in RN Involving the fractional (p, q)-Laplacian / Ambrosio, V.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 32:4(2022). [10.1007/s12220-022-00876-5]

A Kirchhoff Type Equation in RN Involving the fractional (p, q)-Laplacian

Ambrosio V.
2022-01-01

Abstract

In this paper, we deal with the following class of fractional (p, q)-Laplacian Kirchhoff type problem: {(1+[u]s,pp)(-Δ)psu+(1+[u]s,qq)(-Δ)qsu+V(εx)(|u|p-2u+|u|q-2u)=f(u)inRN,u∈Ws,p(RN)∩Ws,q(RN),u>0inRN,where ε> 0 , s∈ (0 , 1) , 1<2q, (-Δ)ts, with t∈ { p, q} , is the fractional t-Laplacian operator, V: RN→ R is a positive continuous potential such that inf ∂ΛV> inf ΛV for some bounded open set Λ ⊂ RN, and f: R→ R is a superlinear continuous nonlinearity with subcritical growth at infinity. By combining the method of Nehari manifold, a penalization technique, and the Lusternik–Schnirelman category theory, we study the multiplicity and concentration properties of solutions for the above problem when ε→ 0.
2022
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/11566/296921
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 5
social impact