次线性函数
数学
拉普拉斯算子
应用数学
纯数学
数学分析
作者
B. Alreshidi,D. D. Hai,R. Shivaji
出处
期刊:Communications on Pure and Applied Analysis
[American Institute of Mathematical Sciences]
日期:2023-01-01
卷期号:22 (9): 2773-2783
摘要
We prove the existence of a positive solution to the $ (p, q) $ Laplacian problem$ \begin{equation*} \left\{ \begin{array}{c} -\Delta _{p}u-\Delta _{q}u=\lambda f(u)\ \text{ in }\Omega , \\ u=0\ \text{ on }\partial \Omega , \end{array} \right. \end{equation*} $where $ \Omega $ is a bounded domain in $ \mathbb{R}^{n} $ with smooth boundary $ \partial \Omega , $ $ p>q>1, \ \Delta _{r}u = div (|\nabla u|^{r-2}\nabla u), \ f:(0, \infty )\rightarrow \mathbb{R\ } $ is continuous, $ p $-sublinear at $ \infty $ and is allowed to be singular at $ 0, $ and $ \lambda >0 $ is a large parameter.
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