In this paper we deal with the stability of solutions to fractional $p$-Laplace problems with nonlinear sources when the fractional parameter $s$ goes to 1. We prove a general convergence result for general weak solutions which is applied to study the convergence of ground state solutions of $p-$fractional problems in bounded and unbounded domains as $s$ goes to 1. Moreover, our result applies to treat the stability of $p-$fractional eigenvalues as $s$ goes to 1.

中文翻译：

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非本地问题解决方案的稳定性

在本文中，我们讨论分数阶解的稳定性 $p$分数参数时非线性源的拉普拉斯问题 $s$ 转到1。我们证明了一般弱解的一般收敛结果，该结果用于研究基态解的收敛。 $p-$有界和无界域中的分数问题 $s$ 转到1。此外，我们的结果适用于治疗 $p-$分数本征值as $s$ 转到1。