Qualitative properties of eigenvectors related to multivalued operators and some existence results (Q1935285)
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scientific article; zbMATH DE number 6136267
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Qualitative properties of eigenvectors related to multivalued operators and some existence results |
scientific article; zbMATH DE number 6136267 |
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Qualitative properties of eigenvectors related to multivalued operators and some existence results (English)
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14 February 2013
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Nonlinear eigenvalue problems related with multivalued discontinuous operators of (extended) Leray-Lions type are studied in this paper by using nonsmooth critical point theory, namely Clarke's generalized gradient. This is carried out in the framework of Banach-Sobolev function spaces with Banach function norms. Several qualitative properties of the corresponding eigenfunctions are also studied, and in particular it is proved that, under some specific conditions, they are actually bounded. One of the main tools for getting these results is relative rearrangement.
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nonlinear eigenvalue problem
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multivalued operator
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Clarke's generalized gradient
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relative rearrangement
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critical point theory
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resonant problem
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