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

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.

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.


2012 ◽  
Vol 86 (2) ◽  
pp. 244-253 ◽  
Author(s):  
YANG-WEN ZHANG ◽  
HONG-XU LI

AbstractIn this paper, we consider the Neumann boundary value problem with a parameter λ∈(0,∞): By using fixed point theorems in a cone, we obtain some existence, multiplicity and nonexistence results for positive solutions in terms of different values of λ. We also prove an existence and uniqueness theorem and show the continuous dependence of solutions on the parameter λ.


2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Dongming Yan ◽  
Qiang Zhang ◽  
Zhigang Pan

We consider the existence of positive solutions for the Neumann boundary value problemx′′(t)+m2(t)x(t)=f(t,x(t))+e(t),t∈(0,    1),x′(0)=0,x′(1)=0, wherem∈C([0,1],(0,+∞)),e∈C[0,1],andf:[0,1]×(0,+∞)→[0,+∞)is continuous. The theorem obtained is very general and complements previous known results.


2007 ◽  
Vol 12 (2) ◽  
pp. 179-186 ◽  
Author(s):  
Svetlana Atslega

We provide multiplicity results for the Neumann boundary value problem, when the second order differential equation is of the form x” = f(x).


2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Hongyu Li ◽  
Junting Zhang

We investigate in this paper the following second-order multipoint boundary value problem:-(Lφ)(t)=λf(t,φ(t)),0≤t≤1,φ′0=0,φ1=∑i=1m-2βiφηi. Under some conditions, we obtain global structure of positive solution set of this boundary value problem and the behavior of positive solutions with respect to parameterλby using global bifurcation method. We also obtain the infinite interval of parameterλabout the existence of positive solution.


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