Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree Approach
In this paper, we develop a general framework for studying Dirichlet Boundary Value Problems (BVP) for second order symmetric implicit differential systems satisfying the Hartman-Nagumo conditions, as well as a certain non-expandability condition. The main result, obtained by means of the equivarian...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2013-11-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2073-8994/5/4/287 |
| _version_ | 1811187713430257664 |
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| author | Mylinh Nguyen Wieslaw Krawcewicz Zhichao Li Zalman Balanov |
| author_facet | Mylinh Nguyen Wieslaw Krawcewicz Zhichao Li Zalman Balanov |
| author_sort | Mylinh Nguyen |
| collection | DOAJ |
| description | In this paper, we develop a general framework for studying Dirichlet Boundary Value Problems (BVP) for second order symmetric implicit differential systems satisfying the Hartman-Nagumo conditions, as well as a certain non-expandability condition. The main result, obtained by means of the equivariant degree theory, establishes the existence of multiple solutions together with a complete description of their symmetric properties. The abstract result is supported by a concrete example of an implicit system respecting D4-symmetries. |
| first_indexed | 2024-04-11T14:07:01Z |
| format | Article |
| id | doaj.art-715f37387ca04fcca7428f9288783d71 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T14:07:01Z |
| publishDate | 2013-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-715f37387ca04fcca7428f9288783d712022-12-22T04:19:51ZengMDPI AGSymmetry2073-89942013-11-015428731210.3390/sym5040287Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree ApproachMylinh NguyenWieslaw KrawcewiczZhichao LiZalman BalanovIn this paper, we develop a general framework for studying Dirichlet Boundary Value Problems (BVP) for second order symmetric implicit differential systems satisfying the Hartman-Nagumo conditions, as well as a certain non-expandability condition. The main result, obtained by means of the equivariant degree theory, establishes the existence of multiple solutions together with a complete description of their symmetric properties. The abstract result is supported by a concrete example of an implicit system respecting D4-symmetries.http://www.mdpi.com/2073-8994/5/4/287symmetric BVPsecond order implicit Ordinary Differential Equation (ODE)multiple solutionsa priori boundsequivariant degreemultivalued mapsdihedral group symmetries |
| spellingShingle | Mylinh Nguyen Wieslaw Krawcewicz Zhichao Li Zalman Balanov Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree Approach Symmetry symmetric BVP second order implicit Ordinary Differential Equation (ODE) multiple solutions a priori bounds equivariant degree multivalued maps dihedral group symmetries |
| title | Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree Approach |
| title_full | Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree Approach |
| title_fullStr | Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree Approach |
| title_full_unstemmed | Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree Approach |
| title_short | Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree Approach |
| title_sort | multiple solutions to implicit symmetric boundary value problems for second order ordinary differential equations odes equivariant degree approach |
| topic | symmetric BVP second order implicit Ordinary Differential Equation (ODE) multiple solutions a priori bounds equivariant degree multivalued maps dihedral group symmetries |
| url | http://www.mdpi.com/2073-8994/5/4/287 |
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