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
Datum:2005
Hauptverfasser: Cano-Casanova, S., Lopez-Gomez, J., Molina-Meyer, M.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2005
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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-124580
record_format dspace
spelling 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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first_indexed 2025-12-02T04:17:41Z
last_indexed 2025-12-02T04:17:41Z
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