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 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 Positive Solutions for Fourth-Order Nonlinear Differential Equation with Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Qi Wang ◽  
Yanping Guo ◽  
Yude Ji
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Fourth Order ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Order Nonlinear Differential Equation ◽  
Existence And Nonexistence

This paper investigates the existence and nonexistence of positive solutions for a class of fourth-order nonlinear differential equation with integral boundary conditions. The associated Green's function for the fourth-order boundary value problems is first given, and the arguments are based on Krasnoselskii's fixed point theorem for operators on a cone.

scholarly journals Positive Solutions for Boundary Value Problems of Fractional Differential Equation with Integral Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Qiao Sun ◽  
Hongwei Ji ◽  
Yujun Cui
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Fractional Differential

By using two fixed-point theorems on cone, we discuss the existence results of positive solutions for the following boundary value problem of fractional differential equation with integral boundary conditions: D0+αx(t)+a(t)f(t,x(t))=0, t∈(0,1), x(0)=x′(0)=0, and x(1)=∫01x(t)dA(t).

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