Sign-Changing Solutions for Fractional Kirchhoff-Type Equations with Critical and Supercritical Nonlinearities

This paper concerns the existence of sign-changing solutions for the following fractional Kirchhoff-type equation with critical and supercritical nonlinearities (a + b[u](2)) (-Delta)(alpha) u + V(x)u = f(x, u) + lambda vertical bar u vertical bar(r-2) u, in R-3, where a, b > 0 are constants, alpha is an element of (3/4, 1), lambda > 0 is a real parameter, r >= 2(alpha)* = 6/3-2 alpha, (-Delta)(alpha) is the fractional Laplace operator, the potential function V and the nonlinearity f satisfy some suitable conditions. By combining an appropriate truncation argument with Moser iteration method, we prove that the existence of sign-changing solutions for the above equation when the parameter lambda is sufficiently small. Our results enrich and improve the previous ones in the literature.