论文标题
liouville型定理，用于半空间
A Liouville-type theorem for the Lane-Emden equation in a half-space
论文作者
论文摘要
我们证明，半空间中车道填充方程的Dirichlet问题没有正常方向单调的阳性溶液。结果，此问题不承认有限条带有任何积极的经典解决方案。这个问题有很长的历史，我们的结果解决了一个长期的开放问题。以前仅适用于有界解决方案，或在非线性中的功率限制下，这种不存在的结果以前可用。结果扩展到一般凸非线性。
We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solution which is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution which is bounded on finite strips. This question has a long history and our result solves a long-standing open problem. Such a nonexistence result was previously available only for bounded solutions, or under a restriction on the power in the nonlinearity. The result extends to general convex nonlinearities.
