In this paper we study the following class of fractional Kirchhoff problems: ε2sM(ε2s−N[u]s2)(−Δ)su+V(x)u=f(u) in RN,u∈Hs(RN),u>0 in RN,where ε>0 is a small parameter, s∈(0,1), N≥2, (−Δ)s is the fractional Laplacian, V:RN→R is a positive continuous function, M:[0,∞)→R is a Kirchhoff function satisfying suitable conditions and f:R→R fulfills Berestycki–Lions type assumptions of subcritical or critical type. Using suitable variational arguments, we prove the existence of a family of positive solutions (uε) which concentrates at a local minimum of V as ε→0.
Concentration phenomena for a class of fractional Kirchhoff equations in RN with general nonlinearities / Ambrosio, V.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 195:(2020), p. 111761. [10.1016/j.na.2020.111761]
Concentration phenomena for a class of fractional Kirchhoff equations in RN with general nonlinearities
Ambrosio V.
2020-01-01
Abstract
In this paper we study the following class of fractional Kirchhoff problems: ε2sM(ε2s−N[u]s2)(−Δ)su+V(x)u=f(u) in RN,u∈Hs(RN),u>0 in RN,where ε>0 is a small parameter, s∈(0,1), N≥2, (−Δ)s is the fractional Laplacian, V:RN→R is a positive continuous function, M:[0,∞)→R is a Kirchhoff function satisfying suitable conditions and f:R→R fulfills Berestycki–Lions type assumptions of subcritical or critical type. Using suitable variational arguments, we prove the existence of a family of positive solutions (uε) which concentrates at a local minimum of V as ε→0.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
