Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension

Marco Squassina; Zhisu Liu; Jianjun Zhang

Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension

Marco Squassina, Zhisu Liu, Jianjun Zhang

Research output: Contribution to journal › Article

Abstract

We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential V . Under suitable assumptions on V , using the monotonicity trick and the profile decomposition, we prove the existence of ground states. In particular, the nonlinearity does not satisfy the Ambrosetti–Rabinowitz type condition or monotonicity assumptions

Original language	English
Pages (from-to)	1-32
Number of pages	32
Journal	NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
Volume	24
Publication status	Published - 2017

Keywords

Kirchhoff equations

Cite this

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title = "Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension",

abstract = "We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential V . Under suitable assumptions on V , using the monotonicity trick and the profile decomposition, we prove the existence of ground states. In particular, the nonlinearity does not satisfy the Ambrosetti–Rabinowitz type condition or monotonicity assumptions",

keywords = "Kirchhoff equations, Kirchhoff equations",

author = "Marco Squassina and Zhisu Liu and Jianjun Zhang",

year = "2017",

language = "English",

volume = "24",

pages = "1--32",

journal = "Nonlinear Differential Equations and Applications",

issn = "1021-9722",

publisher = "Birkhaeuser Verlag AG:Viaduktstrasse 42-44, CH 4051 Basel Switzerland:011 41 61 2050707, EMAIL: subscriptions@birkhauser.ch, INTERNET: http://www.birkhauser.ch, Fax: 011 41 61 2050792",

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TY - JOUR

T1 - Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension

AU - Squassina, Marco

AU - Liu, Zhisu

AU - Zhang, Jianjun

PY - 2017

Y1 - 2017

N2 - We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential V . Under suitable assumptions on V , using the monotonicity trick and the profile decomposition, we prove the existence of ground states. In particular, the nonlinearity does not satisfy the Ambrosetti–Rabinowitz type condition or monotonicity assumptions

AB - We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential V . Under suitable assumptions on V , using the monotonicity trick and the profile decomposition, we prove the existence of ground states. In particular, the nonlinearity does not satisfy the Ambrosetti–Rabinowitz type condition or monotonicity assumptions

KW - Kirchhoff equations

UR - http://hdl.handle.net/10807/132141

M3 - Article

VL - 24

SP - 1

EP - 32

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

SN - 1021-9722

ER -

Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension

Abstract

Keywords

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