scholarly journals Monotone iterative technique and positive solutions to a third-order differential equation with advanced arguments and Stieltjes integral boundary conditions

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Bo Sun
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Order Differential Equation ◽  
Integral Boundary Conditions ◽  
Monotone Iterative Technique ◽  
Stieltjes Integral ◽  
Iterative Technique ◽  
Third Order ◽  
Integral Boundary ◽  
Monotone Iterative

scholarly journals The Solution of Nonlinear Fourth-Order Differential Equation with Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yanli Fu ◽  
Huanmin Yao
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Reproducing Kernel ◽  
Order Differential Equation ◽  
Integral Boundary Conditions ◽  
Reproducing Kernel Space ◽  
Integral Boundary ◽  
Derivatives Of ◽  
Fourth Order Differential Equation

An iterative algorithm is proposed for solving the solution of a nonlinear fourth-order differential equation with integral boundary conditions. Its approximate solutionun(x)is represented in the reproducing kernel space. It is proved thatun(x)converges uniformly to the exact solutionu(x). Moreover, the derivatives ofun(x)are also convergent to the derivatives ofu(x). Numerical results show that the method employed in the paper is valid.

scholarly journals Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hui Li ◽  
Libo Wang ◽  
Minghe Pei
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fourth Order Differential Equation

We investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the formx(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)),t∈[0,1],x(0)=x′(1)=0,x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds,x′′′(1)=0, wheref∈C([0,1]×ℝ4),h∈C([0,1]×ℝ3). By using a fixed point theorem due to D. O'Regan, the existence of solutions and positive solutions for the previous boundary value problems is obtained. Meanwhile, as applications, some examples are given to illustrate our results.

scholarly journals Monotone Iterative Technique and Symmetric Positive Solutions to Fourth-Order Boundary Value Problem with Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Huihui Pang ◽  
Chen Cai
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Symmetric Positive Solutions

The purpose of this paper is to investigate the existence of symmetric positive solutions for a class of fourth-order boundary value problem:u4(t)+βu′′(t)=f(t,u(t),u′′(t)),0<t<1,u(0)=u(1)=∫01‍p(s)u(s)ds,u′′(0)=u′′(1)=∫01‍qsu′′(s)ds, wherep,q∈L1[0,1],f∈C([0,1]×[0,∞)×(-∞,0],[0,∞)). By using a monotone iterative technique, we prove that the above boundary value problem has symmetric positive solutions under certain conditions. In particular, these solutions are obtained via the iteration procedures.

A Fractional q$q$-difference Equation with Integral Boundary Conditions and Comparison Theorem

2017 ◽  
Vol 18 (7-8) ◽  
pp. 575-583 ◽  
Author(s):  
Jing Ren ◽  
Chengbo Zhai
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Comparison Theorem ◽  
Solution Method ◽  
Integral Boundary Conditions ◽  
Monotone Iterative Technique ◽  
Extremal Solutions ◽  
Integral Boundary ◽  
Iterative Schemes ◽  
Monotone Iterative

AbstractIn this article, we mainly prove the existence of extremal solutions for a fractional $q$-difference equation involving Riemann–Lioville type fractional derivative with integral boundary conditions. A comparison theorem under weak conditions is also build, and then we apply the comparison theorem, monotone iterative technique and lower–upper solution method to prove the existence of extremal solutions. Moreover, we can construct two iterative schemes approximating the extremal solutions of the fractional $q$-difference equation with integral boundary conditions. In the last section, a simple example is presented to illustrate the main result.

Sign in / Sign up

Export Citation Format

Share Document