Construction of Solutions for Henon-Type Equation with Critical Growth

We consider the following Henon-type problem with critical growth: {-Delta u = K(vertical bar y'vertical bar,y '')u(2)*(-1), u > 0 in B1, (H) u = 0 on partial derivative B1, where 2* = 2N/N-2, N >= 5, B-1 is the unit sphere in R-N, y = (y', y '') is an element of R-2 x RN-2, r = vertical bar y'vertical bar and K(y)= K(r, y '') is an element of C-2 (B-1) is a bounded non-negative function. By using a finite reduction argument and local Pohozaev-type identities, we prove that if N >= 5 and K(r, y '') has a stable critical point y(0) = (r(0), y(0)'') is an element of partial derivative B-1, then the above problem has infinitely many solutions, whose energy can be arbitrarily large.