Multiple solutions to implicit symmetric boundary value problems for second order ordinary differential equations (ODEs): Equivariant degree approach (Q350663)
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scientific article; zbMATH DE number 6662283
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multiple solutions to implicit symmetric boundary value problems for second order ordinary differential equations (ODEs): Equivariant degree approach |
scientific article; zbMATH DE number 6662283 |
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Multiple solutions to implicit symmetric boundary value problems for second order ordinary differential equations (ODEs): Equivariant degree approach (English)
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9 December 2016
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Summary: 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 \(D_4\)-symmetries.
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symmetric BVP
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second order implicit ordinary differential equation (ODE)
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multiple solutions
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a priori bounds
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equivariant degree
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multivalued maps
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dihedral group symmetries
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