scholarly journals Existence of solutions for a class of fourth-order m-point boundary value problems

2010 ◽  
pp. 1-8
Author(s):  
Jian-Ping Sun ◽  
Qiu-Yan Ren
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Boundary

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)

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.

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