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arXiv · 2507.07664

A New proof of Liouville type theorems for a class of semilinear elliptic equations

Chen Guo·Zhengce Zhang
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Abstract

We study certain typical semilinear elliptic equations in Euclidean space $\bR^{n}$ or on a closed manifold $M$ with nonnegative Ricci curvature. Our proof is based on a crucial integral identity constructed by the invariant tensor method. Together with suitable integral estimates, some classical Liouville theorems will be reestablished.

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Chen Guo, Zhengce Zhang. 2025-07-10. A New proof of Liouville type theorems for a class of semilinear elliptic equations. https://arxiv.org/abs/2507.07664

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