In this paper, we deal with the following fractional Kirchhoff equation egin{equation*} left( p +q(1-s) iint_{mathbb{R}^{2N}} rac{|u(x) - u(y)|^{2}}{|x-y|^{N+2s}} dxdy ight) (-Delta)^{s}u = g(u) &mbox{ in } mathbb{R}^{N}, end{equation*} where $sin (0, 1)$, $Ngeq 2$, $p>0$, $q$ is a small positive parameter and $g:mathbb{R} ightarrow mathbb{R}$ is an odd function satisfying Berestycki–Lions type assumptions. By using minimax arguments, we establish a multiplicity result for the above equation, provided that q is sufficiently small.

A multiplicity result for a fractional Kirchhoff equation in $mathbb{R}^{N}$ with a general nonlinearity / Ambrosio, Vincenzo; Isernia, Teresa. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 20:5(2018), p. 1750054. [10.1142/S0219199717500547]

A multiplicity result for a fractional Kirchhoff equation in $mathbb{R}^{N}$ with a general nonlinearity

Ambrosio, Vincenzo;Isernia, Teresa
2018-01-01

Abstract

In this paper, we deal with the following fractional Kirchhoff equation egin{equation*} left( p +q(1-s) iint_{mathbb{R}^{2N}} rac{|u(x) - u(y)|^{2}}{|x-y|^{N+2s}} dxdy ight) (-Delta)^{s}u = g(u) &mbox{ in } mathbb{R}^{N}, end{equation*} where $sin (0, 1)$, $Ngeq 2$, $p>0$, $q$ is a small positive parameter and $g:mathbb{R} ightarrow mathbb{R}$ is an odd function satisfying Berestycki–Lions type assumptions. By using minimax arguments, we establish a multiplicity result for the above equation, provided that q is sufficiently small.
2018
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/265028
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