We study decay and compact support properties of positive and bounded solutions of ${\mathrm{\Delta }}_{p}u\ge \mathrm{\Lambda }(u)$ on the exterior of a compact set of a complete manifold with rotational symmetry. In the same setting, we also give a new characterization of stochastic completeness for the p-Laplacian in terms of a global $W^{1,p}$-regularity of such solutions. One of the tools we use is a nonlinear version of the Feller property which we investigate on general Riemannian manifolds and which we establish under integral Ricci curvature conditions.

中文翻译：

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非线性PDE的有界子解的定性性质。

我们研究了正解和有界解的衰减和紧支撑特性 ${\mathrm{\Delta }}_pü\ge \mathrm{\Lambda }（ü）$在具有旋转对称性的完整集管的紧凑集的外部。在相同的情况下，我们还根据全局变量对p -Laplacian的随机完整性进行了新的刻画。${\mathrm{w\; ^}}^{\mathrm{1个}，p}$-此类解决方案的规范性。我们使用的工具之一是Feller属性的非线性版本，我们在常规黎曼流形上进行了研究，并在积分Ricci曲率条件下建立了该版本。