Sign-changing solutions for some class of elliptic system

This paper is concerned with the existence of multiple non-radial sign-changing solutions for - Delta u + u + alpha K(vertical bar x vertical bar) Phi(x)u = vertical bar u vertical bar(p-2)u, x is an element of R-3, - Delta Phi = K(vertical bar x vertical bar)u(2), x is an element of R-3, where 2 < p < 6, alpha < 0 can be regarded as a parameter and K(r)(r = vertical bar x vertical bar) is a positive continuous function. We proved that the above equation possesses a non-radial sign-changing solutions with exactly k maximum points and k minimum points for suitable range of alpha.