scholarly journals Positive solutions of four-point boundary value problem for fourth order ordinary differential equation

2010 ◽  
Vol 52 (1-2) ◽  
pp. 200-206 ◽  
Author(s):  
Changchun Yu ◽  
Shihua Chen ◽  
Francis Austin ◽  
Jinhu Lü
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Boundary Value ◽  
Point Boundary ◽  
Order Ordinary Differential Equation

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.

On one two-point BVP for the fourth order linear ordinary differential equation

2017 ◽  
Vol 24 (2) ◽  
pp. 265-275
Author(s):  
Sulkhan Mukhigulashvili ◽  
Mariam Manjikashvili
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Homogeneous Problem ◽  
Sufficient Conditions ◽  
Linear Ordinary Differential Equation ◽  
Point Boundary ◽  
Order Linear

AbstractIn this article we consider the two-point boundary value problem\left\{\begin{aligned} &\displaystyle u^{(4)}(t)=p(t)u(t)+h(t)\quad\text{for }% a\leq t\leq b,\\ &\displaystyle u^{(i)}(a)=c_{1i},\quad u^{(i)}(b)=c_{2i}\quad(i=0,1),\end{% aligned}\right.where {c_{1i},c_{2i}\in R}, {h,p\in L([a,b];R)}. Here we study the question of dimension of the space of nonzero solutions and oscillatory behaviors of nonzero solutions on the interval {[a,b]} for the corresponding homogeneous problem, and establish efficient sufficient conditions of solvability for the nonhomogeneous problem.

scholarly journals The Existence of Positive Solutions for a Nonlinear Sixth-Order Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Wanjun Li ◽  
Liyuan Zhang ◽  
Yukun An
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sixth Order ◽  
Order Ordinary Differential Equation ◽  
Existence Of Positive Solutions ◽  
Bifurcation Methods

By using the Krein-Rutman theorem and bifurcation methods, we discuss the existence of positive solutions for the boundary value problems of a sixth-order ordinary differential equation.

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