Abstract

We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first $q-$eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the $q-$spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.

中文翻译：

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次线性 Lane-Emden 方程的正解是孤立的

摘要

我们证明了在光滑有界集上，具有次线性幂的 Lane-Emden 方程的正最小能量解是孤立的。作为推论，我们得到第一个$q-$Dirichlet-Laplacian 的特征值不是 $q-$谱，在光滑有界集上。我们的结果也扩展到了合适的 Lipschitz 域类别。