Free nonlinear vibrations for plate equations on the equilateral triangle (Q5935776)

The paper deals with the boundary value problem NEWLINE\[NEWLINE\begin{gathered} u_{tt}(t,x)+\triangle ^2u(t,x)-a(\mu)u(t,x)=h(\mu ,x,u),\tag{1} \\ u(t,x)=\triangle u(t,x)=0,\quad x\in \partial \Omega, \end{gathered} NEWLINE\]NEWLINE on \(\mathbb R\times \Omega\) for the equilateral triangle \(\Omega\). (1) describes vibrations of the plate on the equilateral triangle \(\Omega\). It is assumed that \(u=0\) is a trivial solution of (1). Under additional assumptions, there are derived many results on the existence of nonzero time periodic solutions (1) which are either spatially symmetric on the equilateral triangle \(\Omega\) or not. Those results are based on former bifurcation methods of the authors.