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

Zhisu Liu; Marco Squassina; Jianjun Zhang

doi:10.1007/s00030-017-0473-7

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

Zhisu Liu
, Marco Squassina^*
, Jianjun Zhang

^*Corresponding author

University of South China
Chongqing Jiaotong University

Research output: Contribution to journal › Article

30 Citations (Scopus)

Abstract

We study the existence of ground states to a nonlinear fractional\r\nKirchhoff equation with an external potential V . Under suitable assumptions on V , using the monotonicity trick and the profile decomposition, we\r\nprove the existence of ground states. In particular, the nonlinearity does\r\nnot satisfy the Ambrosetti–Rabinowitz type condition or monotonicity\r\nassumptions

Original language	English
Pages (from-to)	1-32
Number of pages	32
Journal	NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
Volume	24
Issue number	4
DOIs	https://doi.org/10.1007/s00030-017-0473-7
Publication status	Published - 2017

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

Kirchhoff equations

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10.1007/s00030-017-0473-7

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abstract = "We study the existence of ground states to a nonlinear fractional\textbackslash{}r\textbackslash{}nKirchhoff equation with an external potential V . Under suitable assumptions on V , using the monotonicity trick and the profile decomposition, we\textbackslash{}r\textbackslash{}nprove the existence of ground states. In particular, the nonlinearity does\textbackslash{}r\textbackslash{}nnot satisfy the Ambrosetti{\textendash}Rabinowitz type condition or monotonicity\textbackslash{}r\textbackslash{}nassumptions",

keywords = "Kirchhoff equations, Kirchhoff equations",

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

year = "2017",

doi = "10.1007/s00030-017-0473-7",

language = "English",

volume = "24",

pages = "1--32",

journal = "NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS",

issn = "1021-9722",

publisher = "Birkhaeuser Verlag AG:Viaduktstrasse 42-44, CH 4051 Basel Switzerland:011 41 61 2050707, EMAIL: [email protected], 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 - Liu, Zhisu

AU - Squassina, Marco

AU - Zhang, Jianjun

PY - 2017

Y1 - 2017

N2 - We study the existence of ground states to a nonlinear fractional\r\nKirchhoff equation with an external potential V . Under suitable assumptions on V , using the monotonicity trick and the profile decomposition, we\r\nprove the existence of ground states. In particular, the nonlinearity does\r\nnot satisfy the Ambrosetti–Rabinowitz type condition or monotonicity\r\nassumptions

AB - We study the existence of ground states to a nonlinear fractional\r\nKirchhoff equation with an external potential V . Under suitable assumptions on V , using the monotonicity trick and the profile decomposition, we\r\nprove the existence of ground states. In particular, the nonlinearity does\r\nnot satisfy the Ambrosetti–Rabinowitz type condition or monotonicity\r\nassumptions

KW - Kirchhoff equations

UR - https://publicatt.unicatt.it/handle/10807/132141

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85026327306&origin=inward

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U2 - 10.1007/s00030-017-0473-7

DO - 10.1007/s00030-017-0473-7

M3 - Article

SN - 1021-9722

VL - 24

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JO - NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS

JF - NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS

IS - 4

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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