scholarly journals Existence results for a class of high order differential equation associated with integral boundary conditions at resonance

2017 ◽  
pp. 111-130
Author(s):  
Le Cong Nhan ◽  
Do Huy Hoang ◽  
Le Xuan Truong
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Order Differential Equation ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
High Order ◽  
Integral Boundary ◽  
At Resonance

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.

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