Sobolev Inequality and the Exact Multiplicity of Solutions and Positive Solutions to a Second-Order Neumann Boundary Value Problem

被引：2
|
作者：
Feng, Yuqiang [1 ,2 ]
机构：
[1] Wuhan Univ Sci & Technol, Sch Sci, Wuhan 430065, Peoples R China
[2] Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China
来源：
ACTA APPLICANDAE MATHEMATICAE | 2010年 / 110卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Neumann boundary value problem; Sobolev inequality; Solution; Exact multiplicity; DIFFERENTIAL-EQUATIONS; PERIODIC-SOLUTIONS; RESONANCE;
D O I：
10.1007/s10440-009-9484-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the exact number of solutions and positive solutions for a second-order Neumann boundary value problem is considered. The exact multiplicity results for this problem are established by Sobolev inequality, comparison theorem, maximum principle and lower and upper solutions method.
引用
收藏
页码：895 / 905
页数：11
相关论文
共 50 条
  • [1] Sobolev Inequality and the Exact Multiplicity of Solutions and Positive Solutions to a Second-Order Neumann Boundary Value Problem
    Yuqiang Feng
    Acta Applicandae Mathematicae, 2010, 110 : 895 - 905
  • [2] Exact multiplicity and stability of solutions of second-order Neumann boundary value problem
    Xing, Hui
    Chen, Hongbin
    He, Xibing
    APPLIED MATHEMATICS AND COMPUTATION, 2014, 232 : 1104 - 1111
  • [3] EXACT THREE POSITIVE SOLUTIONS TO A SECOND-ORDER NEUMANN BOUNDARY VALUE PROBLEM WITH SINGULAR NONLINEARITY
    Feng, Yuqiang
    Li, Guangjun
    ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, 2010, 35 (2D): : 189 - 195
  • [4] POSITIVE SOLUTIONS OF A SECOND-ORDER NEUMANN BOUNDARY VALUE PROBLEM WITH A PARAMETER
    Zhang, Yang-Wen
    Li, Hong-Xu
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2012, 86 (02) : 244 - 253
  • [5] A Singular Nonlinear Second-Order Neumann Boundary Value Problem with Positive Solutions
    Wang, Feng
    Cui, Yunjun
    Zhang, Fang
    THAI JOURNAL OF MATHEMATICS, 2009, 7 (02): : 243 - 257
  • [6] THREE POSITIVE SOLUTIONS TO SECOND-ORDER IMPULSIVE NEUMANN BOUNDARY VALUE PROBLEM
    Sanhui Liu
    Jianli Li
    Annals of Applied Mathematics, 2013, (03) : 288 - 294
  • [7] Existence of positive solutions of superlinear second-order Neumann boundary value problem
    Li Zhilong
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (06) : 3216 - 3221
  • [8] The Existence and Multiplicity of Positive Solutions for Second-Order Periodic Boundary Value Problem
    Wang, Feng
    Zhang, Fang
    Wang, Fuli
    JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2012,
  • [9] Exact multiplicity of solutions for discrete second order Neumann boundary value problems
    Dingyong Bai
    Hairong Lian
    Haiyan Wang
    Boundary Value Problems, 2015
  • [10] Exact multiplicity of solutions for discrete second order Neumann boundary value problems
    Bai, Dingyong
    Lian, Hairong
    Wang, Haiyan
    BOUNDARY VALUE PROBLEMS, 2015, : 1 - 17
12345