We consider a class of a nonlocal heterogeneous elliptic problem of type$$\begin{aligned} -M(|u|_{q}^{q})\,div(a(x)\nabla u)=g(x,u) \end{aligned}$$with a homogeneous Dirichlet boundary condition. Under different assumptions on the function g, we establish two existence theorems for this problem by using, respectively, the Schauder and Tychonoff fixed point theorems. Also, we give an example for each theorem.

中文翻译：

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非局部异质椭圆问题解的存在性

我们考虑一类类型为$$ \ begin {aligned} -M（| u | _ {q} ^ {q}）\，div（a（x）\ nabla u）= g（x ，u）\ end {aligned} $$具有齐次Dirichlet边界条件。在函数g的不同假设下，我们分别通过使用Schauder和Tychonoff不动点定理建立了该问题的两个存在性定理。另外，我们为每个定理给出一个例子。