Semilinear elliptic equations of the Hénon-type in hyperbolic space (Q2796988)
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scientific article; zbMATH DE number 6561301
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Semilinear elliptic equations of the Hénon-type in hyperbolic space |
scientific article; zbMATH DE number 6561301 |
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Semilinear elliptic equations of the Hénon-type in hyperbolic space (English)
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30 March 2016
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Hénon problem
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hyperbolic space
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Sobolev with weights
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positive solutions
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Mountain pass theorem
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The paper deals with a class of semilinear elliptic equations of Hénon type in hyperbolic spaces. The problem involves a logarithm weight in the Poincaré ball model, bringing singularities on the boundary. Considering radial functions, a compact Sobolev embedding result is proved, which extends a former result by \textit{W.-M. Ni} [Indiana Univ. Math. J. 31, 801--807 (1982; Zbl 0515.35033)] proved in the unit ball of \(\mathbb R^N\). Combining this compactness embedding with the Mountain Pass Theorem, the authors establish existence of positive solutions.
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