INFINITELY MANY SOLUTIONS FOR QUASILINEAR EQUATIONS WITH CRITICAL EXPONENT AND HARDY POTENTIAL IN RN

In this paper, we consider the following critical quasilinear equation with Hardy potential: {-Sigma(N)(i,j=1) D-j (a(ij) (u) D(i)u) + 1/2 Sigma(N)(i,j=1) a'(ij) (u) D(i)uD(j)u + a(x)u = nu vertical bar u vertical bar(q-2)u + mu u/vertical bar x vertical bar(2) + vertical bar u vertical bar(2)*(-2)u, in R-N, u(x) -> 0 as vertical bar x vertical bar -> infinity, (1) where a(ij)(u) is an element of C-1(R,R), nu >0, 0 <= mu < alpha<(mu)over bar>, and max{alpha(mu) over bar gamma/alpha(mu) over bar-mu + 2,2* - 2/N-2 root(mu) over bar-mu/alpha} < q < 2*, alpha, gamma > 0, (mu) over bar = (N-2)(2)/4, 2* = 2N/N-2 is the Sobolev critical exponent. And a(x) is a finite, positive potential function satisfying suitable decay assumptions. By using truncation method combining with the regularization approximation approach and compactness arguments, we prove the existence of infinitely many solutions for this equation.