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# On a P–laplace Equation with Multiple Critical Nonlinearities

@inproceedings{PucciOnAP, title={On a P–laplace Equation with Multiple Critical Nonlinearities}, author={Patrizia Pucci} }

Using the Mountain–Pass Theorem of Ambrosetti and Rabinowitz we prove that −∆pu − µ|x| −p u p−1 = |x| −s u p ⋆ (s)−1 + u p ⋆ −1 admits a positive weak solution in R n of class D p 1 (R n)∩ C 1 (R n \ {0}), whenever 0 ≤ µ < µ 1 , and µ 1 = [(n−p)/p] p. Also the case µ < 0 is covered, with a further mild restriction on s when n < p 2. The technique is based on the existence of extremals of some Hardy–Sobolev type embeddings of independent interest. We also show that if u ∈ D p

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