Using the sub-supersolution method, we study the existence of positive solutions for the anisotropic problem 0.1 $$\begin{aligned} -\sum _{i=1}^N\frac{\partial }{\partial x_i}\left( \left| \frac{\partial u}{\partial x_i}\right| ^{p_i-2}\frac{\partial u}{\partial x_i}\right) =\lambda u^{q-1} \end{aligned}$$ - ∑ i = 1 N ∂ ∂ x i ∂ u ∂ x i p i - 2 ∂ u ∂ x i = λ u q - 1 where $$\Omega $$ Ω is a bounded and regular domain of $${\mathbb {R}}^N$$ R N , $$q>1$$ q > 1 , and $$\lambda >0$$ λ > 0 .

中文翻译：

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通过亚超解法对各向异性椭圆算子存在正本征函数

使用子超解法，我们研究了各向异性问题 0.1 $$\begin{aligned} -\sum _{i=1}^N\frac{\partial }{\partial x_i}\left 的正解的存在性( \left| \frac{\partial u}{\partial x_i}\right| ^{p_i-2}\frac{\partial u}{\partial x_i}\right) =\lambda u^{q-1} \end{aligned}$$ - ∑ i = 1 N ∂ ∂ xi ∂ u ∂ xipi - 2 ∂ u ∂ xi = λ uq - 1 其中 $$\Omega $$ Ω 是 $${\ mathbb {R}}^N$$ RN 、 $$q>1$$ q > 1 和 $$\lambda >0$$ λ > 0 。