论文标题
部分可观测时空混沌系统的无模型预测
Semilinear elliptic equations on manifolds with nonnegative Ricci curvature
论文作者
论文摘要
在本文中，我们证明了针对亚临界和临界半线性椭圆方程的解决方案的分类结果，其在非负RICCI曲率的非绘制歧管上具有非负潜力。在下临界情况下，我们表明所有非负解决方案都消失了。此外，在某些自然假设下，在关键情况下，我们证明了强烈的刚性结果，即我们对所有非平凡溶液进行了分类，表明它们仅在电势是恒定的情况下才存在并且歧管是欧几里得空间等均衡的。
In this paper we prove classification results for solutions to subcritical and critical semilinear elliptic equations with a nonnegative potential on noncompact manifolds with nonnegative Ricci curvature. We show in the subcritical case that all nonnegative solutions vanish identically. Moreover, under some natural assumptions, in the critical case we prove a strong rigidity result, namely we classify all nontrivial solutions showing that they exist only if the potential is constant and the manifold is isometric to the Euclidean space.
