Multiple solutions for critical quasilinear elliptic equations

We study the existence of infinitely many solutions for the following quasilinear elliptic equations with critical growth: {- Sigma(N)(i, j = 1) Dj (bi (j) (v) D(i)v) + 1/2 Sigma(N)(i, j = 1) b'(i j) (v)D(i)vD(j)v = a vertical bar v vertical bar(2s-2v) + vertical bar v vertical bar(2sN/N-2) (- 2) v, in Omega, v = 0, on partial derivative Omega, (P) where b(i j) is an element of C-1(R, R) satisfies the growth condition vertical bar b(i j) (t)vertical bar similar to vertical bar t vertical bar(2s-2) at infinity, s >= 1, Omega subset of R-N is an open bounded domain with smooth boundary, a is a constant. Here we use the notations: D-i = partial derivative/partial derivative x(i), b'(i j) (t) = db(i j) (t)/dt. We will study the effect of the terms a vertical bar v vertical bar(2s-2)v and b(i j) (v) on the existence of an unbounded sequence of solutions for (P). Here, we do not assume the crucial global monotone condition. We overcome the difficulties caused by the lack of such monotone condition by performing various kinds of changes of variables.