Multiple solutions of positively homogeneous equations (Q1612549)

The authors study the existence and multiplicity of periodic solutions to the following system \[ u''- Au + \mu u^+ - \nu u^- = v + h(t), \] where \(h\) is a continuous and \(T\)-periodic function, \(v\in \mathbb{R}^N\), and \(A\) is a symmetric matrix. The main results are the following: (1) Under some reasonable assumptions, this system has at least \(2^N\) periodic solutions; (2) If such assumptions do not hold, they construct a system such that it has less than \(2^N\) periodic solutions.