A nonexistence result for anisotropic problemsThe authors are very grateful to the referee for his valuable remarks and suggestions, which helped us improve the paper.,Nonlinearity

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A nonexistence result for anisotropic problemsThe authors are very grateful to the referee for his valuable remarks and suggestions, which helped us improve the paper.
Nonlinearity ( IF 1.7 ) Pub Date : 2020-11-10 , DOI: 10.1088/1361-6544/abaca1
Phuong Le ₁ , Kim Anh T Le ₁ , Phuoc Vinh Dinh ₂

Affiliation

We study the anisotropic problem $-\sum _{i=1}^{N}\frac{\partial }{\partial {x}_{i}}\left({\left\vert \frac{\partial u}{\partial {x}_{i}}\right\vert }^{{p}_{i}-2}\frac{\partial u}{\partial {x}_{i}}\right)=wf\left(u\right)\enspace \text{in}\;{\Omega},\enspace u=0\enspace \;\text{on}\;\partial {\Omega},$ where p _i ⩾ 2, Ω is a domain of ${\mathbb{R}}^{N}$ , w is a nonnegative function and f is an increasing function. We prove that the problem has no nontrivial stable solution under various assumptions on p _i, Ω, w and f.

中文翻译：

各向异性问题的不存在结果作者非常感谢裁判的宝贵意见和建议，这有助于我们改进论文。

我们研究了各向异性的问题 $-\ sum _ {i = 1} ^ {N} \ frac {\ partial} {\ partial {x} _ {i}} \ left（{\ left \ vert \ frac {\ partial u} {\ partial { x} _ {i}} \ right \ vert} ^ {{p} _ {i} -2} \ frac {\ partial u} {\ partial {x} _ {i}} \ right）= wf \ left（ u \ right）\ enspace \ text {in} \; {\ Omega}，\ enspace u = 0 \ enspace \; \ text {on} \; \ partial {\ Omega}，$ ，其中p _我⩾2，Ω是一个域名，w ^是负函数和˚F是增函数。我们证明，在关于p _i，Ω，w和f的各种假设下，该问题没有非平凡的稳定解。 ${\ mathbb {R}} ^ {N}$

更新日期：2020-11-10

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