scholarly journals On positive solution to multi-point fractional h-sum eigenvalue problems for caputo fractional h-difference equations

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2933-2951
Author(s):  
Saowaluck Chasreechai ◽  
Jarunee Soontharanon ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Eigenvalue Problem ◽  
Difference Equation ◽  
Positive Solution ◽  
Point Theorem ◽  
Difference Equations ◽  
Eigenvalue Problems

In this article, we study the existence of at least one positive solution to a multi-point fractional h-sum eigenvalue problem for Caputo fractional h-difference equation, by using the Guo-Krasnoselskii?s fixed point theorem. Moreover, we present some examples to display the importance of these results.

scholarly journals Existence of a positive solution for annth order boundary value problem for nonlinear difference equations

1997 ◽  
Vol 2 (3-4) ◽  
pp. 271-279 ◽  
Author(s):  
Johnny Henderson ◽  
Susan D. Lauer
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Point Theorem ◽  
Difference Equations ◽  
Boundary Value ◽  
Nonlinear Difference Equations

Thenth order eigenvalue problem:                                         Δnx(t)=(−1)n−kλf(t,x(t)),          t∈[0,T],x(0)=x(1)=⋯=x(k−1)=x(T+k+1)=⋯=x(T+n)=0,is considered, wheren≥2andk∈{1,2,…,n−1}are given. Eigenvaluesλare determined forfcontinuous and the case where the limitsf0(t)=limn→0+f(t,u)uandf∞(t)=limn→∞f(t,u)uexist for allt∈[0,T]. Guo's fixed point theorem is applied to operators defined on annular regions in a cone.

scholarly journals Existence and Uniqueness of Positive Solution for Discrete Multipoint Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huili Ma ◽  
Huifang Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems

It is expected in this paper to investigate the existence and uniqueness of positive solution for the following difference equation: -Δ2u(t-1)=f(t,   u(t))+g(t,   u(t)),  t∈Z1,  T, subject to boundary conditions either u(0)-βΔu(0)=0, u(T+1)=αu(η) or Δu(0)=0, u(T+1)=αu(η), where 0<α<1,   β>0,  and   η∈Z2,T-1. The proof of the main result is based upon a fixed point theorem of a sum operator. It is expected in this paper not only to establish existence and uniqueness of positive solution, but also to show a way to construct a series to approximate it by iteration.

scholarly journals Two periodic solutions of neutral difference equations modelling physiological processes

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Wu ◽  
Yicheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Difference Equations ◽  
Neutral Difference Equations ◽  
First Order ◽  
Analysis Techniques ◽  
Physiological Processes

We establish existence, multiplicity, and nonexistence of periodic solutions for a class of first-order neutral difference equations modelling physiological processes and conditions. Our approach is based on a fixed point theorem in cones as well as some analysis techniques.

scholarly journals A Coupled System of Fractional Difference Equations with Nonlocal Fractional Sum Boundary Conditions on the Discrete Half-Line

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 256 ◽  
Author(s):  
Jarunee Soontharanon ◽  
Saowaluck Chasreechai ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Difference Equations ◽  
Existence Result ◽  
Coupled System ◽  
Half Line ◽  
Fractional Difference ◽  
Fractional Difference Equations

In this article, we propose a coupled system of fractional difference equations with nonlocal fractional sum boundary conditions on the discrete half-line and study its existence result by using Schauder’s fixed point theorem. An example is provided to illustrate the results.

scholarly journals Dynamic equations x(Δm)(t) = f(t, x(t)) on time scales

2011 ◽  
Vol 44 (2) ◽  
Author(s):  
Aneta Sikorska-Nowak
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Point Theorem ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Dynamic Equations ◽  
Sadovskii Fixed Point Theorem

AbstractIn this paper we prove the existence of solutions and Carathéodory’s type solutions of the dynamic Cauchy problemThe Sadovskii fixed point theorem and Ambrosetti’s lemma are used to prove the main result.As dynamic equations are an unification of differential and difference equations our result is also valid for differential and difference equations. The results presented in this paper are new not only for Banach valued functions but also for real valued functions.

scholarly journals Asymptotic Stability Results for Nonlinear Fractional Difference Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Fulai Chen ◽  
Zhigang Liu
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Difference Equations ◽  
Stability Of Solutions ◽  
Fractional Difference ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Difference Equations ◽  
Stability Results

We present some results for the asymptotic stability of solutions for nonlinear fractional difference equations involvingRiemann-Liouville-likedifference operator. The results are obtained by using Krasnoselskii's fixed point theorem and discrete Arzela-Ascoli's theorem. Three examples are also provided to illustrate our main results.

scholarly journals Existence of Positive Solution for a Singular Fourth–Order Differential System

2021 ◽  
Vol 18 (2) ◽  
pp. 47-60
Author(s):  
B. Kovács
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Differential System ◽  
Point Theorem ◽  
Fourth Order ◽  
Existence Of Positive Solutions ◽  
Cone Expansion And Compression ◽  
Compression Type

Abstract This paper investigates the existence of positive solutions for a fourth-order differential system using a fixed point theorem of cone expansion and compression type.

scholarly journals Existence of Positive Solution for the Eighth-Order Boundary Value Problem Using Classical Version of Leray–Schauder Alternative Fixed Point Theorem

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 129 ◽  
Author(s):  
Thenmozhi Shanmugam ◽  
Marudai Muthiah ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Eighth Order ◽  
Classical Version ◽  
Nonlinear Alternative

In this work, we investigate the existence of solutions for the particular type of the eighth-order boundary value problem. We prove our results using classical version of Leray–Schauder nonlinear alternative fixed point theorem. Also we produce a few examples to illustrate our results.

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