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.

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.

Monotone iterative technique for impulsive Riemann-Liouville fractional differential equations

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3381-3395 ◽  
Author(s):  
Renu Chaudhary ◽  
Dwijendra Pandey
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Measure Of Noncompactness ◽  
Semigroup Theory ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Fractional Differential

In this article, Monotone iterative technique coupled with the method of lower and upper solutions is employed to discuss the existence and uniqueness of mild solution to an impulsive Riemann-Liouville fractional differential equation. The results are obtained using the concept of measure of noncompactness, semigroup theory and generalized Gronwall inequality for fractional differential equations. At last, an example is given to illustrate the applications of the main results.

scholarly journals Analysis and Computation of Solutions for a Class of Nonlinear SBVPs Arising in Epitaxial Growth

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 774
Author(s):  
Amit K Verma ◽  
Biswajit Pandit ◽  
Ravi P. Agarwal
Keyword(s):  
Differential Equation ◽  
Molecular Beam ◽  
Upper And Lower Solutions ◽  
Elliptic Partial Differential Equation ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Radial Solutions ◽  
Qualitative Properties ◽  
Monotone Iterative ◽  
Singular Ordinary Differential Equation

In this work, the existence and nonexistence of stationary radial solutions to the elliptic partial differential equation arising in the molecular beam epitaxy are studied. Since we are interested in radial solutions, we focus on the fourth-order singular ordinary differential equation. It is non-self adjoint, it does not have exact solutions, and it admits multiple solutions. Here, λ∈R measures the intensity of the flux and G is stationary flux. The solution depends on the size of the parameter λ. We use a monotone iterative technique and integral equations along with upper and lower solutions to prove that solutions exist. We establish the qualitative properties of the solutions and provide bounds for the values of the parameter λ, which help us to separate existence from nonexistence. These results complement some existing results in the literature. To verify the analytical results, we also propose a new computational iterative technique and use it to verify the bounds on λ and the dependence of solutions for these computed bounds on λ.

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.

scholarly journals Monotone iterative technique for nonlinear differential equation of fractional order

2021 ◽  
Author(s):  
Zhengzhi Lu ◽  
Li Yongjun ◽  
Xiaoyan Shi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Iteration Method ◽  
Existence Of Solution ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iteration ◽  
Monotone Iterative ◽  
Fractional Differential ◽  
The Fixed Point Theorem

In this paper, we mainly study the existence of solution of fractional differential equations. Firstly, the existence of the maxmum solution and minmum solution of the differential equation are proved by using the fixed point theorem and the monotone iteration method. Secondly, the existence of the solution of the original equation is proved by using the newly constructed differential equation. Finally, the application of the monotone iteration method is given through an example.

scholarly journals Existence Theory for Positive Iterative Solutions to a Type of Boundary Value Problem

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1585
Author(s):  
Bo Sun
Keyword(s):  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Monotone Iterative Technique ◽  
Existence Theory ◽  
Iterative Technique ◽  
Third Order ◽  
Research Results ◽  
Monotone Iterative ◽  
Iterative Solutions

We introduce some research results on a type of third-order boundary value problem for positive iterative solutions. The existence of solutions to these problems was proved using the monotone iterative technique. As an examination of the proposed method, an example to illustrate the effectiveness of our results was presented.

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.

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