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Laplace’s equation with concave and convex boundary nonlinearities on an exterior region

文献类型:期刊论文

作者Mao,Jinxiu; Zhao,Zengqin; Qian,Aixia
刊名Boundary Value Problems
出版日期2019-03-13
卷号2019期号:1
关键词Exterior regions Laplace operator Concave and convex mixed nonlinear boundary conditions Fountain theorems Steklov eigenvalue problems 35J20 35J65 46E22 49R99
ISSN号1687-2770
DOI10.1186/s13661-019-1163-7
英文摘要AbstractThis paper studies Laplace’s equation ?Δu=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$-\Delta u=0$\end{document} in an exterior region U?RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$U\varsubsetneq {\mathbb{R}}^{N}$\end{document}, when N≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$N\geq 3$\end{document}, subject to the nonlinear boundary condition ?u?ν=λ|u|q?2u+μ|u|p?2u\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{\partial u}{\partial \nu }=\lambda \vert u \vert ^{q-2}u+\mu \vert u \vert ^{p-2}u$\end{document} on ?U with 10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda >0$\end{document} and μ∈R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mu \in \mathbb{R}$\end{document} arbitrary, then there exists a sequence {uk}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{u_{k} \}$\end{document} of solutions with negative energy converging to 0 as k→∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$k\to \infty $\end{document}; on the other hand, when λ∈R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda \in \mathbb{R}$\end{document} and μ>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mu >0$\end{document} arbitrary, then there exists a sequence {u?k}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{\tilde{u}_{k} \}$\end{document} of solutions with positive and unbounded energy. Also, associated with the p-Laplacian equation ?Δpu=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$-\Delta _{p} u=0$\end{document}, the exterior p-harmonic Steklov eigenvalue problems are described.
语种英语
WOS记录号BMC:10.1186/S13661-019-1163-7
出版者Springer International Publishing
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/32524]  
专题中国科学院数学与系统科学研究院
通讯作者Mao,Jinxiu
作者单位
推荐引用方式
GB/T 7714
Mao,Jinxiu,Zhao,Zengqin,Qian,Aixia. Laplace’s equation with concave and convex boundary nonlinearities on an exterior region[J]. Boundary Value Problems,2019,2019(1).
APA Mao,Jinxiu,Zhao,Zengqin,&Qian,Aixia.(2019).Laplace’s equation with concave and convex boundary nonlinearities on an exterior region.Boundary Value Problems,2019(1).
MLA Mao,Jinxiu,et al."Laplace’s equation with concave and convex boundary nonlinearities on an exterior region".Boundary Value Problems 2019.1(2019).

入库方式: OAI收割

来源:数学与系统科学研究院

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