scholarly journals Existence Theorems for a Fourth Order Boundary Value Problem

2009 ◽  
Vol 57 (2) ◽  
pp. 135-148
Author(s):  
A. El-Haffaf
Keyword(s):  
Boundary Value Problem ◽  
Fourth Order ◽  
Existence Theorems ◽  
Boundary Value

scholarly journals Positive Solutions for a Fourth-Order Riemann–Stieltjes Integral Boundary Value Problem

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Yujun Cui ◽  
Donal O’Regan ◽  
Jiafa Xu
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Existence Theorems ◽  
Boundary Value ◽  
Linear Operators ◽  
Stieltjes Integral ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Existence Of Positive Solutions

In this paper, we use the fixed point index to study the existence of positive solutions for the fourth-order Riemann–Stieltjes integral boundary value problem −x4t=ft,xt,x′t,x″t,x″′t, t∈0,1x0=x′0=x″′1=0,x″0=αx″t, where f: 0,1×ℝ+×ℝ+×ℝ+×ℝ+⟶ℝ+ is a continuous function and αx″ denotes a linear function. Two existence theorems are obtained with some appropriate inequality conditions on the nonlinearity f, which involve the spectral radius of related linear operators. These conditions allow ft,z1,z2,z3,z4 to have superlinear or sublinear growth in zi,  i=1,2,3,4.

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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