On the linear and nonlinear discrete second-order Neumann boundary value problems

2014 ◽  
Vol 233 ◽  
pp. 62-71 ◽  
Author(s):  
Chenghua Gao
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Second Order ◽  
Linear And Nonlinear ◽  
Neumann Boundary Value Problems

scholarly journals Parameter Dependence of Positive Solutions for Second-Order Singular Neumann Boundary Value Problems with Impulsive Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Xuemei Zhang
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Second Order ◽  
Impulsive Effects ◽  
Parameter Dependence ◽  
Neumann Boundary Value Problem ◽  
Neumann Boundary Value Problems

The author considers the Neumann boundary value problem-y′′t+Myt=λωtft,yt,  t∈J,    t≠tk,  -Δy′|t=tk=λIktk,ytk,   k=1,2,…,m,  y′(0)=y′(1)=0and establishes the dependence results of the solution on the parameterλ, which cover equations without impulsive effects and are compared with some recent results by Nieto and O’Regan.

scholarly journals Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ruyun Ma ◽  
Chenghua Gao ◽  
Yanqiong Lu
Keyword(s):  
Weight Function ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Negative Eigenvalue ◽  
Second Order ◽  
Negative Eigenvalues ◽  
Positive Elements ◽  
Neumann Boundary Value Problems ◽  
Spectrum Structure

We study the spectrum structure of discrete second-order Neumann boundary value problems (NBVPs) with sign-changing weight. We apply the properties of characteristic determinant of the NBVPs to show that the spectrum consists of real and simple eigenvalues; the number of positive eigenvalues is equal to the number of positive elements in the weight function, and the number of negative eigenvalues is equal to the number of negative elements in the weight function. We also show that the eigenfunction corresponding to thejth positive/negative eigenvalue changes its sign exactlyj-1times.

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