Hardy–Sobolev inequalities in half-space and some semilinear elliptic equations with singular coefficients |
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Authors: | Shaowei Chen Shujie Li |
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Affiliation: | 1. Department of Mathematics, Fujian Normal University, Fuzhou 350007, PR China;2. Institute of Mathematics, Academy of Mathematics and System Science, Academia Sinica, Beijing 100080, PR China |
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Abstract: | We study some semilinear elliptic equations with singular coefficients which relate to some Hardy–Sobolev inequalities. We obtain some existence results for these equations and give a theorem for prescribing the Palais–Smale sequence for these equations. Moreover, we find some interesting connections between these equations and some semilinear elliptic equations in hyperbolic space. Using these connections, we obtain many new results for these equations. |
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Keywords: | 35J20 35J70 |
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