Existence of solutions of three-point boundary value problems for nonlinear fourth order differential equation

1996 ◽  
Vol 17 (6) ◽  
pp. 569-576 ◽  
Author(s):  
Gao Yongxin
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
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.

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)

An extremum variational principle and error estimate procedure for qIV = f(q, x)

1982 ◽  
Vol 92 (2) ◽  
pp. 307-316 ◽  
Author(s):  
Dj. S. Djukic ◽  
T. M. Atanackovic
Keyword(s):  
Differential Equation ◽  
Variational Principle ◽  
Error Estimate ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Estimate Procedure ◽  
Fourth Order Differential Equation

AbstractAn extremum variational principle for boundary value problems described by a non-linear fourth order differential equation qIV = f(q, x) is constructed. For approximate solutions an error estimate procedure, based on the value of the functional, is developed and applied to two concrete problems.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

EXISTENCE THEOREMS OF POSITIVE SOLUTIONS FOR FOURTH-ORDER FOUR-POINT BOUNDARY VALUE PROBLEMS

2004 ◽  
Vol 02 (01) ◽  
pp. 71-85 ◽  
Author(s):  
YUJI LIU ◽  
WEIGAO GE
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
Existence Theorems ◽  
Boundary Value ◽  
Growth Conditions ◽  
Point Boundary ◽  
Order Ordinary Differential Equation ◽  
Order Four

In this paper, we study four-point boundary value problems for a fourth-order ordinary differential equation of the form [Formula: see text] with one of the following boundary conditions: [Formula: see text] or [Formula: see text] Growth conditions on f which guarantee existence of at least three positive solutions for the problems (E)–(B1) and (E)–(B2) are imposed.

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.

scholarly journals A note on solvability of three-point bound-ary value problems for third-order differential equations with p-Laplacian

2008 ◽  
Vol 39 (1) ◽  
pp. 95-103
Author(s):  
XingYuan Liu ◽  
Yuji Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Third Order ◽  
Third Order Differential Equation

Third-point boundary value problems for third-order differential equation$ \begin{cases} & [q(t)\phi(x''(t))]'+kx'(t)+g(t,x(t),x'(t))=p(t),\;\;t\in (0,1),\\ &x'(0)=x'(1)=x(\eta)=0. \end{cases} $is considered. Sufficient conditions for the existence of at least one solution of above problem are established. Some known results are improved.

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