On systems of elliptic equations involving subcritical or critical Sobolev exponents (Q1582397)
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scientific article; zbMATH DE number 1513294
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On systems of elliptic equations involving subcritical or critical Sobolev exponents |
scientific article; zbMATH DE number 1513294 |
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On systems of elliptic equations involving subcritical or critical Sobolev exponents (English)
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27 March 2001
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Existence and non-existence results of positive solutions for a system of elliptic equations with Dirichlet boundary data in a bounded domain with smooth boundary are considered. A non-existence result is proved when \(\Omega\) is star shaped, using some type of Pohozaev identity for a system. Many comparisons with the corresponding scalar case of the problem treated by \textit{H. Brezis} and {L. Nirenberg} [Commun. Pure Appl. Math. 36, 437-477 (1983; Zbl 0541.35029)] are given.
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elliptic systems
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critical Sobolev exponent
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Palais-Smale condition
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mountain pass theorem
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