We use an approximation method to prove the existence of nontrivial weak solutions for two nonlocal inhomogeneous elliptic problems in a bounded domain \(\Omega \) of \({\mathbb {R}}^n \, (n\ge 1)\) under weak conditions on the diffusion coefficients M, \(N: (0,+\infty )\rightarrow {\mathbb {R}}\) and some hypotheses on the \(n\times n\) matrix function a and the functions f, \(g: \Omega \times {\mathbb {R}}\rightarrow {\mathbb {R}}\) that we will give below. Moreover, the existence of a positive solution is obtained for each problem by imposing some additional conditions on \(\Omega \), a, f, g and using a bootstrap argument.

我们使用近似方法来证明在\({\mathbb {R}}^n \, (n\ge 1)\的有界域\(\Omega \)中两个非局部非齐次椭圆问题的非平凡弱解的存在性)在扩散系数M 的弱条件下，\(N: (0,+\infty )\rightarrow {\mathbb {R}}\)和对\(n\times n\)矩阵函数a 的一些假设和函数f , \(g: \Omega \times {\mathbb {R}}\rightarrow {\mathbb {R}}\)我们将在下面给出。此外，通过在\(\Omega \)上施加一些附加条件，可以为每个问题获得正解的存在性，a, f , g并使用引导程序参数。