scholarly journals Three Positive Solutions of Multi-point BVPs for Difference Equations with the Nonlinearity Depending on Δ−operator

2012 ◽  
Vol 20 (3) ◽  
pp. 65-82
Author(s):  
Yuji Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Positive Solutions ◽  
Difference Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Type Boundary ◽  
Discrete Type

Abstract This article deals with a class of discrete type boundary value problems. Sufficient conditions guaranteeing the existence of at least three positive solutions of this class of boundary value problems are established by using a fixed point theorem in cones in Banach spaces. An example is given to illustrate the main theorem.

scholarly journals Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

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 to a Second-Order Discrete Boundary Value Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaojie Lin ◽  
Wenbin Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
The Fixed Point Theorem

We are concerned with second-order discrete boundary value problems and obtain some sufficient conditions for the existence of at least one positive solution by using the fixed point theorem due to Krasnosel'skii on a cone.

scholarly journals Positive solutions of boundary value problems for $ p $-Laplacian functional difference equations

2007 ◽  
Vol 38 (4) ◽  
pp. 291-299
Author(s):  
Changxiu Song
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Functional Difference ◽  
Functional Difference Equation ◽  
Functional Difference Equations

In this paper, the author studies the boundary value problems of $ p $-Laplacian functional difference equation. By using a fixed point theorem in cones, sufficient conditions are established for the existence of the positive solutions.

scholarly journals Existence of Triple Positive Solutions for Second-Order Discrete Boundary Value Problems

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Yanping Guo ◽  
Jiehua Zhang ◽  
Yude Ji
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Triple Positive Solutions

By using a new fixed-point theorem introduced by Avery and Peterson (2001), we obtain sufficient conditions for the existence of at least three positive solutions for the equationΔ2x(k−1)+q(k)f(k,x(k),Δx(k))=0, fork∈{1,2,…,n−1}, subject to the following two boundary conditions:x(0)=x(n)=0orx(0)=Δx(n−1)=0, wheren≥3.

scholarly journals Existence of Three Positive Solutions to Somep-Laplacian Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Moulay Rchid Sidi Ammi ◽  
Delfim F. M. Torres
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Boundary Value ◽  
Sufficient Conditions

We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to somep-Laplacian boundary value problems on time scales.

scholarly journals Blow-Up Solutions for a Singular Nonlinear Hadamard Fractional Boundary Value Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Imed Bachar ◽  
Said Mesloub
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Blow Up ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Fractional Boundary Value Problems

We consider singular nonlinear Hadamard fractional boundary value problems. Using properties of Green’s function and a fixed point theorem, we show that the problem has positive solutions which blow up. Finally, some examples are provided to explain the applications of the results.

Singular boundary value problems for P-Laplacian-like equations

1997 ◽  
Vol 127 (5) ◽  
pp. 975-981 ◽  
Author(s):  
D. D. Hai ◽  
Seth F. Oppenheimer
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Nonlinear Boundary Value Problems ◽  
Existence Of Positive Solutions

SynopsisWe consider the existence of positive solutions to a class of singular nonlinear boundary value problems for P-Laplacian-like equations. Our approach is based on the Schauder Fixed-Point Theorem.

scholarly journals POSITIVE SOLUTIONS OF NTH-ORDER BOUNDARY VALUE PROBLEMS WITH INTEGRAL BOUNDARY CONDITIONS

2015 ◽  
Vol 20 (2) ◽  
pp. 188-204 ◽  
Author(s):  
Ilkay Yaslan Karaca ◽  
Fatma Tokmak Fen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Integral Boundary

In this paper, by using double fixed point theorem and a new fixed point theorem, some sufficient conditions for the existence of at least two and at least three positive solutions of an nth-order boundary value problem with integral boundary conditions are established, respectively. We also give two examples to illustrate our main results.

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