In this paper, we study the following nonlinear problem of Kirchhoff type with critical Sobolev exponent: {-(a + b integral(R3) vertical bar Du vertical bar(2)) Delta u + u = f(x, u) + u(5), x is an element of R-3, u is an element of H-1 (R-3), u > 0, x is an element of R-3, where a, b > 0 are constants. Under certain assumptions on the sign-changing function f(x,u), we prove the existence of positive solutions by variational methods. Our main results can be viewed as a partial extension of a recent result of He and Zou in [Journal of Differential Equations, 2012] concerning the existence of p...
