Sign-changing solutions for a fractional Kirchhoff equation

Abstract Using a minimization argument and a quantitative deformation lemma, we establish the existence of least energy sign-changing solutions for the following nonlinear Kirchhoff problem ( a + b [ u ] 2 ) ( − Δ ) s u + V ( x ) u = K ( x ) f ( u ) in R 3 , where a , b > 0 are constants, s ∈ ( 0 , 1 ) , ( − Δ ) s is the fractional Laplacian, V , K are continuous, positive functions, allowed for vanishing behavior at infinity, and f is a continuous function satisfying suitable growth assumptions. Moreover, when the nonlinearity f is odd, we obtain the existence of infinitely many nontrivial weak solutions not necessarily nodals.