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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Опубліковано в: :Український математичний вісник
Дата:2005
Автори: Cano-Casanova, S., Lopez-Gomez, J., Molina-Meyer, M.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут прикладної математики і механіки НАН України 2005
Онлайн доступ: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
Цитувати: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
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author Cano-Casanova, S.
Lopez-Gomez, J.
Molina-Meyer, M.
author_facet Cano-Casanova, S.
Lopez-Gomez, J.
Molina-Meyer, M.
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.
collection DSpace DC
container_title Український математичний вісник
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.
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language English
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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
spellingShingle Bounded Components of Positive Solutions of Nonlinear Abstract Equations
Cano-Casanova, S.
Lopez-Gomez, J.
Molina-Meyer, M.
title 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_short Bounded Components of Positive Solutions of Nonlinear Abstract Equations
title_sort bounded components of positive solutions of nonlinear abstract equations
url https://nasplib.isofts.kiev.ua/handle/123456789/124580
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