On a p-Laplace equation with multiple critical nonlinearities |
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Authors: | Roberta Filippucci Patrizia Pucci Frédéric Robert |
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Affiliation: | 1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, via Vanvitelli 1, 06123 Perugia, Italy;2. Laboratoire J.-A. Dieudonné, Université de Nice–Sophia Antipolis, 06108 Nice Cedex 2, France |
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Abstract: | Using the Mountain-Pass Theorem of Ambrosetti and Rabinowitz we prove that admits a positive weak solution in of class , whenever , and . The technique is based on the existence of extremals of some Hardy–Sobolev type embeddings of independent interest. We also show that if is a weak solution in of , then when either , or and u is also of class . |
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