In this work we prove the existence of standing-wave solutions to the scalar non-linear Klein-Gordon equation in dimension one and the stability of the ground-state, the set which contains all the minima of the energy constrained to the manifold of the states sharing a fixed charge. For non-linearities which are combinations of two competing powers we prove that standing-waves in the ground-state are orbitally stable. We also show the existence of a degenerate minimum and the existence of two positive and radially symmetric minima having the same charge.

中文翻译：

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具有两个竞争幂的标量非线性 Klein-Gordon 方程的多重归一化驻波解

在这项工作中，我们证明了第一维标量非线性 Klein-Gordon 方程的驻波解的存在性和基态的稳定性，该集合包含约束到流形的能量的所有最小值。共享固定费用的州。对于作为两个竞争功率组合的非线性，我们证明了基态驻波在轨道上是稳定的。我们还展示了退化最小值的存在以及两个具有相同电荷的正径向对称最小值的存在。