On the perturbed eigenvalue problem (Q1804777)
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scientific article; zbMATH DE number 755529
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the perturbed eigenvalue problem |
scientific article; zbMATH DE number 755529 |
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On the perturbed eigenvalue problem (English)
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17 August 1995
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The author considers the perturbed eigenvalue problem \(L(x) v(x)= \lambda(x) v(x)\) near \(0= x\in \mathbb{R}\) with \(L(x)\) a Fredholm operator of index zero. Using the implicit function theorem and the bordering lemma, he derives a necessary and sufficient smoothness condition for the characteristic pairs \((\lambda(x), v(x))\) with eigenvalue \(\lambda(x)\) emanating from a semi-simple eigenvalue \(\lambda(0)\) of \(L(0)\).
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perturbed eigenvalue problem
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Fredholm operator of index zero
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implicit function theorem
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bordering lemma
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