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

#### 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.
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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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