%0 Journal Article
%T Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree Approach
%A Zalman Balanov
%A Wieslaw Krawcewicz
%A Zhichao Li
%A Mylinh Nguyen
%J Symmetry
%D 2013
%I MDPI AG
%R 10.3390/sym5040287
%X 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.
%K symmetric BVP
%K second order implicit Ordinary Differential Equation (ODE)
%K multiple solutions
%K a priori bounds
%K equivariant degree
%K multivalued maps
%K dihedral group symmetries
%U http://www.mdpi.com/2073-8994/5/4/287