Multiple solutions to symmetric boundary value problems for second order ODEs: Equivariant degree approach

作者：Balanov Zalman; Krawcewicz Wieslaw^*; My Linh Nguyen

来源：Nonlinear Analysis-Theory Methods & Applications, 2014, 94: 45-64.

DOI：10.1016/j.na.2013.07.030

• Symmetric systems of ODEs
• Multiple solutions
• Boundary value problems
• Equivariant degree

For a long time, a vector nonlinear pendulum equation (VNPE) stands as a paradigmatic example of nonlinear analysis. Under the so-called Hartman-Nagumo conditions, the solvability of the Dirichlet boundary value problem for the VNPE was established by Hartman (using the Schauder Fixed Point Theorem). In this paper, we establish a general framework for studying the impact of symmetries to multiple symmetric solutions to Dirichlet/Neumann BVP for VNPE based on the usage of the equivariant degree method. Abstract results are supported by concrete computations related to VNPE respecting dihedral group symmetries.

• 出版日期2014-1