We study local well-posedness and orbital stability/instability of standing waves for a first order system associated with a nonlinear Klein–Gordon equation on a star graph. The proof of the well-posedness uses a classical fixed point argument and the Hille–Yosida theorem. Stability study relies on the linearization approach and recent results for the NLS equation with the δ-interaction on a star graph.

中文翻译：

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星形图上的非线性 Klein-Gordon 方程

我们研究了与星形图上非线性 Klein-Gordon 方程相关的一阶系统的驻波的局部适定性和轨道稳定性/不稳定性。适定性的证明使用经典不动点论证和 Hille-Yosida 定理。稳定性研究依赖于线性化方法和最近的 NLS 方程与星形图上的 δ 相互作用的结果。