We prove Pohozaev-type identities for smooth solutions of Euler-Lagrange equations of second and fourth order that arise from functional a depending on homogeneous Hörmander vector fields. We then exploit such integral identities to prove non-existence results for the associated boundary value problems.

中文翻译：

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由齐向矢量场驱动的微分算子的Pohozaev型恒等式

我们证明了二阶和四阶Euler-Lagrange方程的光滑解的Pohozaev型恒等式，该光滑解是由函数a取决于齐次Hörmander向量场产生的。然后，我们利用这些积分身份来证明相关边界值问题的不存在结果。