scholarly journals Monotone Iterative Technique for a Class of Slanted Cantilever Beam Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Mei Wei ◽  
Qiang Li
Keyword(s):  
Cantilever Beam ◽  
Existence And Uniqueness ◽  
Elastic Beam ◽  
Monotone Iterative Technique ◽  
Iterative Sequence ◽  
Order Ordinary Differential Equation ◽  
Existence And Uniqueness Results ◽  
Monotone Iterative ◽  
Uniqueness Results ◽  
Beam Equations

In this paper, we deal with the existence and uniqueness of the solutions of two-point boundary value problem of fourth-order ordinary differential equation: u4(t)=f(t,u(t),u′(t)),  t∈[0,1],  u(0)=u′(0)=u′′(1)=u′′′(1)=0, where f:[0,1]×R2→R is a continuous function. The problem describes the static deformation of an elastic beam whose left end-point is fixed and right is freed, which is called slanted cantilever beam. Under some weaker assumptions, we establish a new maximum principle by the perturbation of positive operator and construct the monotone iterative sequence of the lower and upper solutions, and, based on this, we obtain the existence and uniqueness results for the slanted cantilever beam.

scholarly journals Perturbation Results and Monotone Iterative Technique for Fractional Evolution Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
Jia Mu
Keyword(s):  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Ordered Banach Space ◽  
Fractional Evolution Equations ◽  
Existence And Uniqueness Results ◽  
Monotone Iterative ◽  
Fractional Evolution Equation ◽  
Uniqueness Results

We mainly study the fractional evolution equation in an ordered Banach space , , , . Using the monotone iterative technique based on lower and upper solutions, the existence and uniqueness results are obtained. The necessary perturbation results for accomplishing this approach are also developed.

scholarly journals Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
He Yang
Keyword(s):  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Initial Value ◽  
Monotone Iterative ◽  
Uniqueness Results ◽  
Impulsive Evolution Equations

This paper deals with the existence and uniqueness of mild solutions for the initial value problems of abstract impulsive evolution equations in an ordered Banach spaceE:u′(t)+Au(t)=f(t,u(t),Gu(t)),t∈[0,a],t≠tk,Δu|t=tk=Ik(u(tk)),0<t1<t2<⋯<tm<a,u(0)=u0, whereA:D(A)⊂E→Eis a closed linear operator, andf:[0,a]×E×E→Eis a nonlinear mapping. Under wide monotone conditions and measure of noncompactness conditions of nonlinearityf, some existence and uniqueness results are obtained by using a monotone iterative technique in the presence of lower and upper solutions.

scholarly journals Positive Mild Solutions of Periodic Boundary Value Problems for Fractional Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Jia Mu ◽  
Hongxia Fan
Keyword(s):  
Existence And Uniqueness ◽  
Periodic Boundary ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Boundary Value ◽  
Fractional Evolution Equations ◽  
Existence And Uniqueness Results ◽  
Monotone Iterative ◽  
Uniqueness Results ◽  
Periodic Boundary Value Problems

The periodic boundary value problem is discussed for a class of fractional evolution equations. The existence and uniqueness results of mild solutions for the associated linear fractional evolution equations are established, and the spectral radius of resolvent operator is accurately estimated. With the aid of the estimation, the existence and uniqueness results of positive mild solutions are obtained by using the monotone iterative technique. As an application that illustrates the abstract results, an example is given.

scholarly journals Sensitivity analysis of solutions for a system of generalized parametric nonlinear quasivariational inequalities

2005 ◽  
Vol 2005 (11) ◽  
pp. 1795-1807
Author(s):  
Zeqing Liu ◽  
Beibei Zhu ◽  
Shin Min Kang ◽  
Gwang Il Kim
Keyword(s):  
Sensitivity Analysis ◽  
Existence And Uniqueness ◽  
Maximal Monotone ◽  
Iterative Sequence ◽  
Monotone Mappings ◽  
Quasivariational Inequalities ◽  
Existence And Uniqueness Results ◽  
New Class ◽  
Uniqueness Results ◽  
Convergence Results

A new class of system of generalized parametric nonlinear quasivariational inequalities involving various classes of mappings is introduced and studied. With the properties of maximal monotone mappings, the equivalence between the class of system of generalized parametric nonlinear quasivariational inequalities and a class of fixed point problems is proved and an iterative algorithm with errors is constructed. A few existence and uniqueness results and sensitivity analysis of solutions are also established for the system of generalized nonlinear parametric quasivariational inequalities and some convergence results of iterative sequence generated by the algorithm with errors are proved.

scholarly journals Monotone Iterative Technique for the Periodic Solutions of High-Order Delayed Differential Equations in Abstract Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 449
Author(s):  
He Yang ◽  
Yongxiang Li
Keyword(s):  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Upper And Lower Solutions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Order Ordinary Differential Equation ◽  
Monotone Iterative ◽  
Delayed Differential Equations ◽  
Abstract Spaces ◽  
Fixed Delay

This paper deals with the existence of ω-periodic solutions for nth-order ordinary differential equation involving fixed delay in Banach space E. Lnu(t)=f(t,u(t),u(t−τ)),t∈R, where Lnu(t):=u(n)(t)+∑i=0n−1aiu(i)(t), ai∈R, i=0,1,⋯,n−1, are constants, f(t,x,y):R×E×E⟶E is continuous and ω-periodic with respect to t, τ>0. By applying the approach of upper and lower solutions and the monotone iterative technique, some existence and uniqueness theorems are proved under essential conditions.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

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