We study nonhomogeneous elliptic problems considering a general linear elliptic operator with singular critical potentials and nonlinearities depending on multiplier operators that can be derivatives (even fractional) and singular integral operators. The general elliptic operator can contain derivatives of high-order and fractional type like polyharmonic operators and fractional Laplacian. We obtain results about existence and qualitative properties in a space whose norm is based on the Fourier transform. Our approach is of non-variational type and consists in a contraction argument in a critical space for the studied elliptic PDEs. Examples of applications are given.

中文翻译：

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具有临界势和非线性导数项的椭圆方程的傅立叶分析方法

考虑具有奇异临界电势和非线性的一般线性椭圆算子，我们研究非齐次椭圆问题，非线性算子取决于可以是导数（偶数）的乘子算子和奇异积分算子。一般的椭圆算子可以包含高阶和小数类型的导数，例如多谐函数算子和分数拉普拉斯算子。我们获得关于空间的存在和定性性质的结果，该空间的范数基于傅立叶变换。我们的方法是非变分类型的，并且在所研究的椭圆PDE的临界空间中包含一个收缩参数。给出了应用示例。