Existence of Ground State Sign-Changing Solutions of Fractional Kirchhoff-Type Equation with Critical Growth

In this paper, we study the following fractional Kirchhoff-type equation {-(a + b integral(RN) integral(RN) vertical bar u(x) - u(y)vertical bar(2) K (x - y)dxdy)L(K)u = vertical bar u vertical bar(2 alpha)*(-2) u + mu f(u), x is an element of Omega, u = 0, x is an element of R-N\Omega, where Omega subset of R-N is a bounded domain with a smooth boundary, alpha is an element of (0, 1), 2 alpha < N < 4 alpha, 2(alpha)(*)is the fractional critical Sobolev exponent and mu, a, b > 0; LK is nonlocal integrodifferential operator. Under suitable conditions on f, for mu large enough, by using constraint variational method and the quantitative deformation lemma, we obtain a ground state sign-changing (or nodal) solution to this problem, and its energy is strictly larger than twice that of the ground state solutions.