This paper deals with the following class of quasilinear elliptic problems in radial form {-(r(alpha)\u'\(beta)u')' = lambda r(delta)u(l-1) + r(gamma)u(q-1) in (0, R) {u > 0, u(R) = u' (0) = 0 where alpha, beta, delta, l, gamma, q are given real numbers, lambda > 0 is a parameter and 0 < R < infinity. Some results on the existence of positive solutions are obtained by combining the R Mountain Pass Theorem with an argument used by Brezis and Nirenberg to overcome the lack of compactness due to the presence of critical Sobolev exponents.214759