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 S-shaped connected component of positive solutions for second-order discrete Neumann boundary value problems

2020 ◽  
Vol 18 (1) ◽  
pp. 1658-1666
Author(s):  
Liangying Miao ◽  
Jing Liu ◽  
Zhiqian He
Keyword(s):  
Boundary Value Problem ◽  
Weight Function ◽  
Positive Solutions ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Second Order ◽  
Connected Component ◽  
Bifurcation Method ◽  
Neumann Boundary Value Problem ◽  
Neumann Boundary Value Problems

Abstract By using the bifurcation method, we study the existence of an S-shaped connected component in the set of positive solutions for discrete second-order Neumann boundary value problem. By figuring the shape of unbounded connected component of positive solutions, we show that the Neumann boundary value problem has three positive solutions suggesting suitable conditions on the weight function and nonlinearity.

Positive solutions for second-order superlinear repulsive singular Neumann boundary value problems

Positivity ◽  
2008 ◽  
Vol 12 (3) ◽  
pp. 555-569 ◽  
Author(s):  
Jifeng Chu ◽  
Xiaoning Lin ◽  
Daqing Jiang ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Second Order ◽  
Neumann Boundary Value Problems
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