Sign-changing solutions for a fractional Kirchhoff equation

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)su+V(x)u=K(x)f(u)inR3,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.