GENERALIZED ONE-STEP IMPLICIT HYBRID BLOCK METHOD FOR SECOND ORDER DIRICHLET AND NEUMANN BOUNDARY VALUE PROBLEMS

2017 ◽  
Vol 102 (10) ◽  
pp. 2233-2252
Author(s):  
Zurni Omar ◽  
Mohammad Alkasassbeh
2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Xuemei Zhang

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.


2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ruyun Ma ◽  
Chenghua Gao ◽  
Yanqiong Lu

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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