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 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 Applications of Stieltjes Derivatives to Periodic Boundary Value Inclusions

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2142
Author(s):  
Bianca Satco ◽  
George Smyrlis
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Conditions ◽  
Solution Set ◽  
First Order

In the present paper, we are interested in studying first-order Stieltjes differential inclusions with periodic boundary conditions. Relying on recent results obtained by the authors in the single-valued case, the existence of regulated solutions is obtained via the multivalued Bohnenblust–Karlin fixed-point theorem and a result concerning the dependence on the data of the solution set is provided.

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 to Fractional Difference Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Huiqin Chen ◽  
Yaqiong Cui ◽  
Xianglan Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Real Number ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Fractional Difference ◽  
Schäuder Fixed Point Theorem

The following fractional difference boundary value problems▵νyt=-ft+ν-1,yt+ν-1,y(ν-2)=y(ν+b+1)=0are considered, where1<ν≤2is a real number and▵νy(t)is the standard Riemann-Liouville fractional difference. Based on the Krasnosel’skiǐ theorem and the Schauder fixed point theorem, we establish some conditions onfwhich are able to guarantee that this FBVP has at least two positive solutions and one solution, respectively. Our results significantly improve and generalize those in the literature. A number of examples are given to illustrate our main results.

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 Periodic Boundary Value Problems for First-Order Impulsive Functional Integrodifferential Equations with Integral-Jump Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Chatthai Thaiprayoon ◽  
Decha Samana ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problems ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Integrodifferential Equations ◽  
Jump Conditions ◽  
Comparison Result ◽  
First Order ◽  
Monotone Iterative ◽  
Periodic Boundary Value Problems ◽  
Minimal And Maximal Solutions

By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive functional integrodifferential equations with integral-jump conditions. An example is also given to illustrate our results.

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