Abstract We study solvability of some linear nonhomogeneous elliptic problems and establish that under reasonable technical conditions the convergence in L 2 ( R d ) of their right sides implies the existence and the convergence in H 4 ( R d ) of the solutions. The problems contain the squares of the sums of second order non-Fredholm differential operators and we use the methods of the spectral and scattering theory for Schrodinger type operators. We especially emphasize that here we deal with the fourth order operators in contrast to the second order operators in [29] and investigate the dependence of the solvability conditions on the dimension of our problem when the constant a = 0 . We also consider the case of solvability with a single potential in an arbitrary dimension.

中文翻译：

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某些四阶非 Fredholm 算子的序列意义上的可解性

摘要 我们研究了一些线性非齐次椭圆问题的可解性，并确定在合理的技术条件下，它们右侧的L 2 (R d ) 收敛意味着解的H 4 (R d ) 的存在和收敛。这些问题包含二阶非 Fredholm 微分算子的和的平方，我们对 Schrodinger 型算子使用光谱和散射理论的方法。我们特别强调，这里我们处理与 [29] 中的二阶运算符相反的四阶运算符，并研究了当常数 a = 0 时可解性条件对我们问题维度的依赖性。我们还考虑了在任意维度上具有单一势能的可解性情况。