Abstract
For an orthogonal $\Gamma$-representation $V$ ($\Gamma$ is a finite group) and for an even $\Gamma$-invariant $C^2$-functional $f\colon V\to \mathbb R$ satisfying the condition $0< \theta \nabla f(x)\bullet x \leq \nabla^2 f(x)x\bullet x$ (for $\theta> 1$ and $x\in V\setminus \{0\}$), we consider the odd Newtonian system $\ddot x(t)=-\nabla f(x(t))$ and establish the existence of multiple periodic solutions with a minimal period $p$ (for any given $p > 0$). As an example, we prove the existence of arbitrarily many periodic solutions with minimal period $p$ for a specific $D_n$-symmetric Newtonian system.
Citation
Wieslaw Krawcewicz. Yanli Lv. Huafeng Xiao. "Multiple solutions with prescribed minimal period for second order odd Newtonian systems with symmetries." Topol. Methods Nonlinear Anal. 47 (2) 659 - 679, 2016. https://doi.org/10.12775/TMNA.2016.024
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