Bounded Components of Positive Solutions of Nonlinear Abstract Equations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Bounded Components of Positive Solutions of Nonlinear Abstract Equations
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| Creator |
Cano-Casanova, S.
Lopez-Gomez, J. Molina-Meyer, M. |
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| 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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| Date |
2017-09-29T14:23:30Z
2017-09-29T14:23:30Z 2005 |
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| Type |
Article
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| Identifier |
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. http://dspace.nbuv.gov.ua/handle/123456789/124580 |
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| Language |
en
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| Relation |
Український математичний вісник
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| Publisher |
Інститут прикладної математики і механіки НАН України
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