Abstract
The main theorem establishes the existence of a positive decaying solution u ∈ D 0 1,p (Rn) of a quasilinear elliptic problem involving the p-Laplacian operator and the critical Sobolev exponent pN/(N - p), 1<p<N. The conclusion depends on the existence of a lowest eigenvalue of a related quasilinear eigenvalue problem. A preliminary result yields a Palais-Smale compactness condition for an associated functional via concentration-compactness methods of P. L. Lions.
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