The sharp existence of constrained minimizers for a class of nonlinear Kirchhoff equations

In this paper, we study the existence of solutions with prescribed L-2-norm for the following Kirchhoff type equation: -(a + b integral(RN) vertical bar del u vertical bar(2))Delta u -vertical bar u vertical bar(p-2)u =lambda u, x is an element of R-N, lambda is an element of R, where N 0 are constants, p is an element of(2, 2*), 2 = 6 if N = 3, and 2*= +infinity if N = 1, 2. We obtain the sharp existence of global constraint minimizers for 2 < p