A multiplicity result for a fractional Kirchhoff equation in R-N with a general nonlinearity

作者：Ambrosio Vincenzo^*; Isernia Teresa

来源：Communications in Contemporary Mathematics, 2018, 20(5): 1750054.

DOI：10.1142/S0219199717500547

• Stationary Kirchhoff equation
• fractional Laplacian
• variational methods

In this paper, we deal with the following fractional Kirchhoff equation
(p + q(1 - s) integral integral R2N vertical bar u(x) - u(y)vertical bar(2)/vertical bar x - y vertical bar(N+2s) dx dy) (-Delta)(s) u = g(s) in R-N,
where s is an element of(0, 1), N >= 2, p > 0, q is a small positive parameter and g : R -> 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.

• 出版日期2018-8