scholarly journals Existence and Iteration of Positive Solutions to Third-Order BVP for a Class ofp-Laplacian Dynamic Equations on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
A. Kameswara Rao
Keyword(s):  
Positive Solutions ◽  
Time Scales ◽  
Monotone Iterative Technique ◽  
Dynamic Equations ◽  
Laplacian Operator ◽  
Iterative Technique ◽  
Third Order ◽  
Iterative Schemes ◽  
Monotone Iterative ◽  
Existence Of Positive Solutions

We investigate the existence and iteration of positive solutions for the following third-orderp-Laplacian dynamic equations on time scales:(ϕp(uΔΔ(t)))∇+q(t)f(t,u(t),uΔΔ(t))=0,  t∈[a,b],αu(ρ(a))-βuΔ(ρ(a))=0,  γu(b)+δuΔ(b)=0,  uΔΔ(ρ(a))=0,whereϕp(s)isp-Laplacian operator; that is,ϕp(s)=sp-2s,  p>1,  ϕp-1=ϕq, and1/p+1/q=1.By applying the monotone iterative technique and without the assumption of the existence of lower and upper solutions, we not only obtain the existence of positive solutions for the problem, but also establish iterative schemes for approximating the solutions.

scholarly journals Monotone Iterative Technique for Partial Dynamic Equations of First Order on Time Scales

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Peiguang Wang ◽  
Ping Li
Keyword(s):  
Time Scales ◽  
Monotone Iterative Technique ◽  
Dynamic Equations ◽  
Iterative Technique ◽  
First Order ◽  
Monotone Iterative ◽  
Comparison Results

This work is concerned with the monotone iterative technique for partial dynamic equations of first order on time scales and for this purpose, the existence, uniqueness, and comparison results are also established.

scholarly journals Successive Iteration and Positive Solutions for Nonlinearm-Point Boundary Value Problems on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-13
Author(s):  
Yanbin Sang
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Boundary Value ◽  
Point Boundary ◽  
Iterative Schemes ◽  
Monotone Iterative ◽  
Successive Iteration ◽  
Existence Of Positive Solutions ◽  
Cone Expansion And Compression

We study the existence of positive solutions for a class ofm-point boundary value problems on time scales. Our approach is based on the monotone iterative technique and the cone expansion and compression fixed point theorem of norm type. Without the assumption of the existence of lower and upper solutions, we do not only obtain the existence of positive solutions of the problem, but also establish the iterative schemes for approximating the solutions.

scholarly journals Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Fatma Tokmak ◽  
Ilkay Yaslan Karaca
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Third Order ◽  
Existence Of Positive Solutions

A four-functional fixed point theorem and a generalization of Leggett-Williams fixed point theorem are used, respectively, to investigate the existence of at least one positive solution and at least three positive solutions for third-order -point boundary value problem on time scales with an increasing homeomorphism and homomorphism, which generalizes the usual -Laplacian operator. In particular, the nonlinear term is allowed to change sign. As an application, we also give some examples to demonstrate our results.

scholarly journals Existence of Positive Solutions for Multi-Point Boundary Value Problems on Infinite Intervals in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Zhaocai Hao ◽  
Liang Ma
Keyword(s):  
Banach Spaces ◽  
Positive Solutions ◽  
Boundary Value ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Point Boundary ◽  
Monotone Iterative ◽  
Mönch Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Infinite Intervals

We investigate the positive solutions of a class of second-order nonlinear singular differential equations with multi-point boundary value conditions on an infinite interval in Banach spaces. The tools we used are the cone theory and Mönch fixed point theorem and a monotone iterative technique. An example is also given to demonstrate the applications of our results, which include and extend some existing results.

Symmetric positive solutions for the systems of higher-order boundary value problems on time scales

2017 ◽  
Vol 8 (4) ◽  
Author(s):  
Arzu Denk Oğuz ◽  
Fatma Serap Topal
Keyword(s):  
Boundary Value Problems ◽  
Recent Work ◽  
Positive Solutions ◽  
Time Scales ◽  
Boundary Value ◽  
Higher Order ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Symmetric Positive Solutions

AbstractIn this paper, we discuss the existence of symmetric positive solutions for the systems of higher-order boundary value problems on time scales. Our results extend some recent work in the literature. The analysis of this paper mainly relies on the monotone iterative technique.

scholarly journals Positive Solutions for Third-Order Nonlinearp-Laplacianm-Point Boundary Value Problems on Time Scales

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
Fuyi Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Third Order ◽  
Existence Of Positive Solutions

We study the following third-orderp-Laplacianm-point boundary value problems on time scales:(ϕp(uΔ∇))∇+a(t)f(t,u(t))=0,t∈[0,T]T,βu(0)−γuΔ(0)=0,u(T)=∑i=1m−2aiu(ξi),ϕp(uΔ∇(0))=∑i=1m−2biϕp(uΔ∇(ξi)), whereϕp(s)isp-Laplacian operator, that is,ϕp(s)=|s|p−2s,p>1,  ϕp−1=ϕq,1/p+1/q=1,  0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.

scholarly journals Positive Solutions for a Class of p-Laplacian Hadamard Fractional-Order Three-Point Boundary Value Problems

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 308 ◽  
Author(s):  
Jiafa Xu ◽  
Jiqiang Jiang ◽  
Donal O’Regan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Order ◽  
Boundary Value ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Point Boundary ◽  
Monotone Iterative ◽  
Existence Of Positive Solutions

In this paper, using the Avery–Henderson fixed point theorem and the monotone iterative technique, we investigate the existence of positive solutions for a class of p-Laplacian Hadamard fractional-order three-point boundary value problems.

scholarly journals Iterative Solutions for the Differential Equation with p -Laplacian on Infinite Interval

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Guoying Zhao ◽  
Ying Wang
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Monotone Iterative Technique ◽  
Infinite Interval ◽  
Iterative Technique ◽  
Iterative Schemes ◽  
Monotone Iterative ◽  
Existence Of Positive Solutions ◽  
Iterative Solutions ◽  
Fourth Order Differential Equation

This paper systematically investigates a class of fourth-order differential equation with p -Laplacian on infinite interval in Banach space. By means of the monotone iterative technique, we establish not only the existence of positive solutions but also iterative schemes under the suitable conditions. At last, we give an example to demonstrate the application of the main result.

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