We study a generalization of the power of Laplace operator with null Dirichlet conditions by means of the spectral theory and prove several existence results for nonlinear equations with such operators, especially when the problem is resonant. Some regularity results are also obtained.

中文翻译：

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具有广义分数拉普拉斯算子的非线性方程

我们利用谱理论研究了具有零狄里克雷条件的拉普拉斯算子的幂的泛化，并证明了带有此类算子的非线性方程的几个存在性结果，尤其是当问题是共振的时候。还获得一些规律性结果。