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 Positive Solutions for a Mixed-Order Three-Point Boundary Value Problem forp-Laplacian

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Francisco J. Torres
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Main Tool ◽  
Index Theory ◽  
Laplacian Operator ◽  
Existence And Multiplicity ◽  
Fixed Point Index Theory ◽  
Multiplicity Of Positive Solutions

The author investigates the existence and multiplicity of positive solutions for boundary value problem of fractional differential equation withp-Laplacian operator. The main tool is fixed point index theory and Leggett-Williams fixed point theorem.

scholarly journals Positive Solutions for a Fourth-Order Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Kun Wang ◽  
Zhilin Yang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Index Theory ◽  
Existence And Multiplicity ◽  
Fixed Point Index Theory ◽  
Multiplicity Of Positive Solutions

This paper deals with the existence and multiplicity of positive solutions for the fourth-order boundary value problemu(4)=f(t,u,u′,−u′′, u′′′),u(0)=u′(1)=u′′′(0)=u′′(1)=0. Heref∈C([0,1]×ℝ+4,ℝ+)(ℝ+:=[0,+∞)). We use fixed point index theory to establish our main results based on a priori estimates achieved by utilizing some integral identities and integral inequalities.

scholarly journals Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 107
Author(s):  
Daliang Zhao ◽  
Juan Mao
Keyword(s):  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Integral Boundary ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann–Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions f(t,u,v) and g(t,u,v) in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann–Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green’s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results.

scholarly journals Existence and Multiplicity of Positive Solutions for a System of Fourth-Order Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Shoucheng Yu ◽  
Zhilin Yang
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Index Theory ◽  
Existence And Multiplicity ◽  
Fixed Point Index Theory ◽  
Multiplicity Of Positive Solutions

We study the existence and multiplicity of positive solutions for the system of fourth-order boundary value problems x(4)=ft,x,x′,-x′′,-x′′′,y,y′,-y′′,-y′′′,  y(4)=gt,x,x′,-x′′,-x′′′,y,y′,-y′′,-y′′′,  x(0)=x′(1)=x′′(0)=x′′′(1)=0, and y(0)=y′(1)=y′′(0)=y′′′(1)=0, where f,g∈C([0,1]×R+8,R+)  (R+:=[0,∞)). We use fixed point index theory to establish our main results based on a priori estimates achieved by utilizing some integral identities and inequalities and R+2-monotone matrices.

Existence and Multiplicity of Positive Solutions for a Dirichlet Boundary Value Problem in ℝ2

2002 ◽  
Vol 2 (3) ◽  
Author(s):  
V. Barutello ◽  
A. Capietto ◽  
P. Habets
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Degree Theory ◽  
Dirichlet Boundary Value Problem ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
Parameter Dependent ◽  
Vector Differential Equation

AbstractWe deal with the Dirichlet boundary value problem associated to a parameter-dependent second order vector differential equation. Using the method of lower and upper solutions together with degree theory, we provide existence and multiplicity of positive solutions.

scholarly journals The Existence and Multiplicity of Positive Solutions for Second-Order Periodic Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Feng Wang ◽  
Fang Zhang ◽  
Fuli Wang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Periodic Boundary Value Problem ◽  
Point Index ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

The existence and multiplicity of positive solutions are established for second-order periodic boundary value problem. Our results are based on the theory of a fixed point index for A-proper semilinear operators defined on cones due to Cremins. Our approach is different in essence from other papers and the main results of this paper are also new.

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