Summary
The main theorem establishes the existence of a positive decaying solution u ∈ D 1,p0 (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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Supported by NSERC (Canada) under Grant OGP0003105.
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Swanson, C.A., Yu, L.S. Criticalp-Laplacian problems in RN . Annali di Matematica pura ed applicata 169, 233–250 (1995). https://doi.org/10.1007/BF01759355
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DOI: https://doi.org/10.1007/BF01759355