scholarly journals Existence of solutions for fourth order differential equation with four-point boundary conditions

2007 ◽  
Vol 20 (11) ◽  
pp. 1131-1136 ◽  
Author(s):  
Chuanzhi Bai ◽  
Dandan Yang ◽  
Hongbo Zhu
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Existence Of Solutions ◽  
Point Boundary ◽  
Fourth Order Differential Equation

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.

Inclusion of a Support Friction Into a Computerized Solution of a Self-Compensating Pipeline

1972 ◽  
Vol 94 (3) ◽  
pp. 797-802 ◽  
Author(s):  
J. Sobieszczanski
Keyword(s):  
Differential Equation ◽  
Computer Program ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Bending Moment ◽  
Variable Coefficients ◽  
Point Boundary ◽  
Friction Forces ◽  
The One ◽  
Fourth Order Differential Equation

Thermal elongations of a pipeline are compensated in many cases by bending of pipeline branches. If the pipeline lies on a horizontal rough and flat foundation that bending is influenced by friction forces. Analysis of that influence is given in the paper. A nonlinear, fourth order differential equation with variable coefficients governing the phenomenon is derived and solved numerically as a two-point boundary problem. A version of the solution suitable for a pipeline on discrete supports has been developed. It may be used in conjunction with any existing computer program for pipeline stress analysis. The results demonstrate existence of a very significant additional bending moment due to friction. It may exceed several times the one computed for a pipeline on frictionless foundation.

Fourth Order Boundary Value Problems and Comparison Theorems

1961 ◽  
Vol 13 ◽  
pp. 625-638 ◽  
Author(s):  
John H. Barrett
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Comparison Theorems ◽  
Point Boundary ◽  
Image Position

This paper is primarily concerned with the existence of solutions of the fourth-order self-adjoint differential equation(1)(where r(x) > 0, q(x) ≥ 0, p(x) ≥ 0 and all three coefficients are continuous on [a, ∞)) and one of the two-point boundary conditions:(2)or(3)the subscript notation for any solution y(x) denoting:(4)

15.—A Class of Focal Points for Non-self-adjoint Fourth-order Differential Equations

1975 ◽  
Vol 72 (3) ◽  
pp. 207-214
Author(s):  
Kurt Kreith
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Trivial Solution ◽  
General Equation ◽  
Order Differential Equation ◽  
Upper Bounds ◽  
Conjugate Points ◽  
Focal Points ◽  
Fourth Order Differential Equation

SynopsisConjugate points are defined in terms of solutions of a linear fourth-order differential equation satisfying two homogeneous boundary conditions at x = α and either u(β) = u′(β) = 0 or u′(γ) = u″(γ) = 0. The smallest β > α and γ > α such that these boundary conditions are satisfied by a non-trivial solution of the equation are denoted by η(α) and ῆ-(α), respectively. Upper bounds are established for min [η(α), ῆ(α)] relative to the conjugate points of a self-adjoint differential equation which is majorised by the more general equation under study.

The number of Dirichlet solutions of a fourth order differential equation

1982 ◽  
Vol 92 (3-4) ◽  
pp. 233-239 ◽  
Author(s):  
Thomas T. Read
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Differential Expression ◽  
Fourth Order ◽  
Dirichlet Form ◽  
Order Differential Equation ◽  
Dirichlet Integral ◽  
Linearly Independent ◽  
Nondecreasing Functions ◽  
Fourth Order Differential Equation

SynopsisIt is shown that the equation (p2y”)”–(p1y’)’+ p0y = 0 has exactly two linearly independent solutions on [0,∞) with finite Dirichlet integral when the coefficients are nonnegative and p2 satisfies a condition which includes all nondecreasing functions. An inequality for the Dirichlet form is derived and used to extend characterizations of the domains of certain self-adjoint operations associated with the differential expression to arbitrary symmetric boundary conditions at 0.

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