# The Method of Lower and Upper Solutions for Fourth-Order Two-Point Boundary Value Problems

@article{Ruyun1997TheMO, title={The Method of Lower and Upper Solutions for Fourth-Order Two-Point Boundary Value Problems}, author={Ma Ru-yun and Zhang Jihui and Fu Shengmao}, journal={Journal of Mathematical Analysis and Applications}, year={1997}, volume={215}, pages={415-422} }

Abstract In this paper we develop the monotone method in the presence of lower and upper solutions for the problem u (IV) = f(x, u(x), u″(x)), u(0) = u(1) = u″(0) = u″(1) = 0, where f : [0, 1] × R × R → R is continuous.

## 173 Citations

### Multiple Positive Solutions for a Fourth-order Boundary Value Problem

- Mathematics
- 2003

In this paper, we discuss the existence of multiple positive solutions for the fourth-order boundary value problem u(t) = f(t, u(t)), 0 < t < 1, u(0) = u(1) = u′′(0) = u′′(1) = 0, where f : [0, 1]×…

### Multiple Positive Solutions of Fourth-order Boundary Value Problems

- Mathematics
- 2005

In this paper, we discuss the existence of multiple positive solutions for the fourth-order boundary value problem (BVP) u(4)(t) + βu′′(t) = f (t, u(t)), 0 < t < 1, u(0) = u(1) = u′′(0) = u′′(1) = 0,…

### Upper and Lower Solutions Method for Fourth-Order Periodic Boundary Value Problems

- Mathematics
- 2008

Abstract The purpose of this paper is to prove the existence of a solution of the following periodic boundary value problem in the presence of an upper solution β and a lower solution α with β ≤ α,…

### Existence results for some fourth-order multi-point boundary value problem

- MathematicsMath. Comput. Model.
- 2009

### Existence of positive solutions for fourth-order boundary value problem with variable parameters

- Mathematics
- 2007

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

- Mathematics
- 2004

In this paper, we study four-point boundary value problems for a fourth-order ordinary differential equation of the form with one of the following boundary conditions: or Growth conditions on f which…

## References

SHOWING 1-10 OF 24 REFERENCES

### The Method of Lower and Upper Solutions for Second, Third, Fourth, and Higher Order Boundary Value Problems

- Mathematics
- 1994

Abstract In this paper we develop the monotone method in the presence of lower and upper solutions for the problem u (n) (t)=ƒ(t, u(t));u (i) (a)−u (i) (b)=λ i ∈ R ; i=0, ..., n−1. Where ƒ is a…

### A uniqueness theorem for a boundary value problem

- Mathematics
- 1979

In this paper it is proved that the two-point boundary value problem, namely (d(4)/dx4 + fy = g, y(O) A1 = y(l) A2 = Y"(O)BI = y"(l) B2 = 0, has a unique solution provided infxf(x) = i > V4. The…

### NONRESONANCE CONDITIONS FOR FOURTH ORDER NONLINEAR BOUNDARYVALUE PROBLEMS

- Mathematics
- 1994

This paper is devoted to the study of the problem u(O) ,(), ,'(0) u'(9.), u"(O) ,"(2), u"'(O) ,,'"(2).

### Existence for a fourth-order boundary value problem under a two-parameter nonresonance condition

- Mathematics
- 1991

We show existence for a nonlinear fourth-order boundary value problem under a nonresonance condition involving a two-parameter linear eigenvalue problem. We also state extensions of this result to…

### On the Existence of Positive Solutions of Fourth-Order Ordinary Differential Equations

- Mathematics
- 1995

We study the existence of positive rolutioru of the equations with either . We show the existence of at least one positive solution iff is either superlinear or sublinear by a simple application of a…

### Fourth-order two-point boundary value problems

- Mathematics
- 1988

On etablit les theoremes d'existence et d'unicite pour un probleme aux valeurs limites d'ordre 4 lineaire et non lineaire

### Some multiplicity results for an elastic beam equation at resonance

- Mathematics
- 1993

AbstractThis paper deals with multiplicity results for nonlinear elastic equations of the type
$$\begin{gathered} - d^4 u/dx^4 + \pi ^4 u + g(x,u) = e(x) (0< x< 1) \hfill \\ u(0) = u(1) = u''(0) =…