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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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Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75081, USA
* Author to whom correspondence should be addressed.
Received: 29 August 2013 / Revised: 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 (CC BY 3.0).
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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.

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