scholarly journals Multiple Positive Solutions for Singular Semipositone Periodic Boundary Value Problems with Derivative Dependence

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Huiqin Lu
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
First Order ◽  
Periodic Boundary Value Problems ◽  
The Fixed Point Theorem ◽  
Special Cone

By constructing a special cone inC1[0,2π]and the fixed point theorem, this paper investigates second-order singular semipositone periodic boundary value problems with dependence on the first-order derivative and obtains the existence of multiple positive solutions. Further, an example is given to demonstrate the applications of our main results.

scholarly journals Positive Solutions to Periodic Boundary Value Problems for Four-Order Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Huantao Zhu ◽  
Zhiguo Luo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Periodic Boundary Value Problems

We apply fixed point theorem in a cone to obtain sufficient conditions for the existence of single and multiple positive solutions of periodic boundary value problems for a class of four-order differential equations.

scholarly journals Positive Solutions for System of First-Order Dynamic Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
Da-Bin Wang ◽  
Jian-Ping Sun ◽  
Xiao-Jun Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Dynamic Equations ◽  
First Order ◽  
Periodic Boundary Value Problems ◽  
Existence Of Positive Solutions ◽  
Eigenvalue Intervals

We study the existence of positive solutions to the system of nonlinear first-order periodic boundary value problems on time scalesxΔ(t)+P(t)x(σ(t))=F(t,x(σ(t))),t∈[0,T]T,x(0)=x(σ(T)), by using a well-known fixed point theorem in cones. Moreover, we characterize the eigenvalue intervals forxΔ(t)+P(t)x(σ(t))=λH(t)G(x(σ(t))),t∈[0,T]T,x(0)=x(σ(T)).

scholarly journals MULTIPLE SOLUTIONS OF PERIODIC BOUNDARY VALUE PROBLEMS FOR FIRST-ORDER DIFFERENCE EQUATIONS

2008 ◽  
Vol 78 (1) ◽  
pp. 1-11
Author(s):  
DA-BIN WANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Multiple Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Order Difference ◽  
First Order ◽  
Periodic Boundary Value Problems

AbstractIn this paper, existence criteria for multiple solutions of periodic boundary value problems for the first-order difference equation are established by using the Leggett–Williams multiple fixed point theorem and fixed point theorem of cone expansion and compression. Two examples are also given to illustrate the main results.

scholarly journals Positive Solutions of Three-Order Delayed Periodic Boundary Value Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Na Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Point Boundary ◽  
Periodic Boundary Value Problems ◽  
Existence Of Positive Solutions ◽  
Existence And Nonexistence ◽  
The Fixed Point Theorem

Our main purpose is to consider the existence of positive solutions for three-order two-point boundary value problem in the following form: u′′′(t)+ρ3u(t)=f(t,u(t-τ)),  0≤t≤2π,  u(i)(0)=u(i)(2π),  i=1,2,  u(t)=σ,  -τ≤t≤0, where σ,ρ, and τ are given constants satisfying τ∈(0,π/2). Some inequality conditions on ρ3u-f(t,u) guaranteeing the existence and nonexistence of positive solutions are presented. Our discussion is based on the fixed point theorem in cones.

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