scholarly journals A global bifurcation theorem for a positone multiparameter problem and its application

2017 ◽  
Vol 37 (10) ◽  
pp. 5127-5149 ◽  
Author(s):  
Kuo-Chih Hung ◽  
◽  
Shao-Yuan Huang ◽  
Shin-Hwa Wang ◽  
◽  
...  
Keyword(s):  
Global Bifurcation ◽  
Bifurcation Theorem ◽  
Multiparameter Problem

scholarly journals A global bifurcation theorem for critical values in Banach spaces

2018 ◽  
Vol 198 (3) ◽  
pp. 773-794
Author(s):  
Pablo Amster ◽  
Pierluigi Benevieri ◽  
Julián Haddad
Keyword(s):  
Banach Spaces ◽  
Global Bifurcation ◽  
Critical Values ◽  
Bifurcation Theorem

scholarly journals A global bifurcation theorem for Darwinian matrix models

2016 ◽  
Vol 22 (8) ◽  
pp. 1114-1136 ◽  
Author(s):  
Emily P. Meissen ◽  
Kehinde R. Salau ◽  
Jim M. Cushing
Keyword(s):  
Matrix Models ◽  
Global Bifurcation ◽  
Bifurcation Theorem

scholarly journals Existence of Positive Solutions of a Discrete Elastic Beam Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Ruyun Ma ◽  
Jiemei Li ◽  
Chenghua Gao
Keyword(s):  
Positive Solutions ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Global Bifurcation ◽  
Elastic Beam ◽  
Beam Equation ◽  
Nonlinear Boundary Value Problems ◽  
Order Difference ◽  
Bifurcation Theorem ◽  
Existence Of Positive Solutions

LetTbe an integer withT≥5and letT2={2,3,…,T}. We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equationsΔ4u(t−2)−ra(t)f(u(t))=0,t∈T2,u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, whereris a constant,a:T2→(0,∞),  and  f:[0,∞)→[0,∞)is continuous. Our approaches are based on the Krein-Rutman theorem and the global bifurcation theorem.

scholarly journals Bifurcation Behaviors of Steady-State Solution to a Discrete General Brusselator Model

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Ruyun Ma ◽  
Zhongzi Zhao
Keyword(s):  
A Priori ◽  
Global Bifurcation ◽  
Small Neighborhood ◽  
Steady State Solution ◽  
Solution Curve ◽  
Bifurcation Theorem ◽  
Brusselator Model ◽  
Constant Solution ◽  
A Priori Estimation ◽  
Increasing Function

We study the local and global bifurcation of nonnegative nonconstant solutions of a discrete general Brusselator model. We generalize the linear u in the standard Brusselator model to the nonlinear fu. Assume that f∈C0,∞,0,∞ is a strictly increasing function, and f′f−1a∈0,∞. Taking b as the bifurcation parameter, we obtain that the solution set of the problem constitutes a constant solution curve and a nonconstant solution curve in a small neighborhood of the bifurcation point b0j,f−1a,ab/f−1a2. Moreover, via the Rabinowitz bifurcation theorem, we obtain the global structure of the set of nonconstant solutions under the condition that fs/s2 is nonincreasing in 0,∞. In this process, we also make a priori estimation for the nonnegative nonconstant solutions of the problem.

scholarly journals Global Bifurcation for Second-Order Neumann Problem with a Set-Valued Term

2009 ◽  
Vol 2009 ◽  
pp. 1-16
Author(s):  
Ruyun Ma ◽  
Jiemei Li
Keyword(s):  
Neumann Problem ◽  
Differential Inclusion ◽  
Line Segment ◽  
Global Bifurcation ◽  
Second Order ◽  
Approximation Procedure ◽  
Bifurcation Theorem ◽  
Jump Discontinuities ◽  
Sturm Liouville

We study the global bifurcation of the differential inclusion of the form−(ku′)′+g(⋅,u)∈μF(⋅,u),  u′(0)=0=u′(1), whereFis a “set-valued representation” of a function with jump discontinuities along the line segment[0,1]×{0}. The proof relies on a Sturm-Liouville version of Rabinowitz's bifurcation theorem and an approximation procedure.

scholarly journals Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth-Order Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Ruyun Ma ◽  
Yanqiong Lu
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Boundary Value ◽  
Global Bifurcation ◽  
Main Tool ◽  
Bifurcation Theorem ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

we show the existence and multiplicity of positive solutions of the nonlinear discrete fourth-order boundary value problemΔ4ut-2=λhtfut,t∈T2,u1=uT+1=Δ2u0=Δ2uT=0, whereλ>0,h:T2→(0,∞)is continuous, andf:R→[0,∞)is continuous,T>4,T2=2,3,…,T. The main tool is the Dancer's global bifurcation theorem.

scholarly journals Nodal Solutions for Some Second-Order Semipositone Integral Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huiqin Lu ◽  
Yang Wang ◽  
Yansheng Liu
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Global Bifurcation ◽  
Second Order ◽  
Nodal Solutions ◽  
Integral Boundary ◽  
Bifurcation Theorem ◽  
Existence And Multiplicity ◽  
Integral Boundary Value Problems

Using bifurcation techniques, we first prove a global bifurcation theorem for nonlinear second-order semipositone integral boundary value problems. Then the existence and multiplicity of nodal solutions of the above problems are obtained. Finally, an example is worked out to illustrate our main results.

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