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Symmetry 2013, 5(4), 287-312; doi:10.3390/sym5040287
Article

Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree Approach

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Received: 29 August 2013; in revised form: 24 October 2013 / Accepted: 28 October 2013 / Published: 7 November 2013
(This article belongs to the Special Issue Symmetry Breaking)
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Abstract: 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.
Keywords: symmetric BVP; second order implicit Ordinary Differential Equation (ODE); multiple solutions; a priori bounds; equivariant degree; multivalued maps; dihedral group symmetries symmetric BVP; second order implicit Ordinary Differential Equation (ODE); multiple solutions; a priori bounds; equivariant degree; multivalued maps; dihedral group symmetries
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Balanov, Z.; Krawcewicz, W.; Li, Z.; Nguyen, M. Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree Approach. Symmetry 2013, 5, 287-312.

AMA Style

Balanov Z, Krawcewicz W, Li Z, Nguyen M. Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree Approach. Symmetry. 2013; 5(4):287-312.

Chicago/Turabian Style

Balanov, Zalman; Krawcewicz, Wieslaw; Li, Zhichao; Nguyen, Mylinh. 2013. "Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree Approach." Symmetry 5, no. 4: 287-312.


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