Bounded Components of Positive Solutions of Nonlinear Abstract Equations
In this work a general class of nonlinear abstract equations satisfying a generalized strong maximum principle is considered in order to show that any bounded component of positive solutions bifurcating from the curve of trivial states (λ, u) = (λ, 0) at a nonlinear eigenvalue λ = λ₀ must meet the c...
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| Veröffentlicht in: | Український математичний вісник |
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| Datum: | 2005 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2005
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/124580 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Bounded Components of Positive Solutions of Nonlinear Abstract Equations / S. Cano-Casanova, J. Lopez-Gomez, M. Molina-Meyer // Український математичний вісник. — 2005. — Т. 2, № 1. — С. 38-51. — Бібліогр.: 13 назв. — англ. |
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Cano-Casanova, S. Lopez-Gomez, J. Molina-Meyer, M. 2017-09-29T14:23:30Z 2017-09-29T14:23:30Z 2005 Bounded Components of Positive Solutions of Nonlinear Abstract Equations / S. Cano-Casanova, J. Lopez-Gomez, M. Molina-Meyer // Український математичний вісник. — 2005. — Т. 2, № 1. — С. 38-51. — Бібліогр.: 13 назв. — англ. 1810-3200 2000 MSC. 34A34, 34C23, 35B32, 35B50, 35J25. https://nasplib.isofts.kiev.ua/handle/123456789/124580 In this work a general class of nonlinear abstract equations satisfying a generalized strong maximum principle is considered in order to show that any bounded component of positive solutions bifurcating from the curve of trivial states (λ, u) = (λ, 0) at a nonlinear eigenvalue λ = λ₀ must meet the curve of trivial states (λ, 0) at another singular value λ₁ ≠ λ₀. Since the unilateral theorems of P. H. Rabinowitz [13, Theorems 1.27 and 1.40] are not true as originally stated (c.f. the counterexample of E. N. Dancer [6]), in order to get our main result the unilateral theorem of J. Lopez-Gomez [11, Theorem 6.4.3] is required. en Інститут прикладної математики і механіки НАН України Український математичний вісник Bounded Components of Positive Solutions of Nonlinear Abstract Equations Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Bounded Components of Positive Solutions of Nonlinear Abstract Equations |
| spellingShingle |
Bounded Components of Positive Solutions of Nonlinear Abstract Equations Cano-Casanova, S. Lopez-Gomez, J. Molina-Meyer, M. |
| title_short |
Bounded Components of Positive Solutions of Nonlinear Abstract Equations |
| title_full |
Bounded Components of Positive Solutions of Nonlinear Abstract Equations |
| title_fullStr |
Bounded Components of Positive Solutions of Nonlinear Abstract Equations |
| title_full_unstemmed |
Bounded Components of Positive Solutions of Nonlinear Abstract Equations |
| title_sort |
bounded components of positive solutions of nonlinear abstract equations |
| author |
Cano-Casanova, S. Lopez-Gomez, J. Molina-Meyer, M. |
| author_facet |
Cano-Casanova, S. Lopez-Gomez, J. Molina-Meyer, M. |
| publishDate |
2005 |
| language |
English |
| container_title |
Український математичний вісник |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
In this work a general class of nonlinear abstract equations satisfying a generalized strong maximum principle is considered in order to show that any bounded component of positive solutions bifurcating from the curve of trivial states (λ, u) = (λ, 0) at a nonlinear eigenvalue λ = λ₀ must meet the curve of trivial states (λ, 0) at another singular value λ₁ ≠ λ₀. Since the unilateral theorems of P. H. Rabinowitz [13, Theorems 1.27 and 1.40] are not true as originally stated (c.f. the counterexample of E. N. Dancer [6]), in order to get our main result the unilateral theorem of J. Lopez-Gomez [11, Theorem 6.4.3] is required.
|
| issn |
1810-3200 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/124580 |
| citation_txt |
Bounded Components of Positive Solutions of Nonlinear Abstract Equations / S. Cano-Casanova, J. Lopez-Gomez, M. Molina-Meyer // Український математичний вісник. — 2005. — Т. 2, № 1. — С. 38-51. — Бібліогр.: 13 назв. — англ. |
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AT canocasanovas boundedcomponentsofpositivesolutionsofnonlinearabstractequations AT lopezgomezj boundedcomponentsofpositivesolutionsofnonlinearabstractequations AT molinameyerm boundedcomponentsofpositivesolutionsofnonlinearabstractequations |
| first_indexed |
2025-12-02T04:17:41Z |
| last_indexed |
2025-12-02T04:17:41Z |
| _version_ |
1850861547077763072 |