A remark on multiple solutions for a nonlinear eigenvalue problem (Q959459)
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scientific article; zbMATH DE number 5381763
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A remark on multiple solutions for a nonlinear eigenvalue problem |
scientific article; zbMATH DE number 5381763 |
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A remark on multiple solutions for a nonlinear eigenvalue problem (English)
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11 December 2008
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Existence of multiple solutions is obtained for systems of the type \(Bu=\lambda F(u)\), where \(B\) is a definite positive matrix and \(F\) is either ``superquadratic'' or ``subquadratic'' and also in ``diagonal'' form with each component odd. The main tool used in the proof is Clark's theorem in critical point theory. Several examples and counterexamples are provided in order to show that results are sharp and also that some previous results are not correct.
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nonlinear algebraic system
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critical point theory
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multiple solutions
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