y

IJPAM: Volume 70, No. 4 (2011)

THE UPPER AND LOWER SOLUTION METHOD FOR
NONLINEAR FOURTH-ORDER THREE-POINT
BOUNDARY VALUE PROBLEM

A. Elhaffaf$^1$, M. Naceri$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Oran University
BP1524, Es-Senia, ALGERIA


Abstract. This paper is concerned with the following fourth-order three-point boundary value problem

\begin{eqnarray*} \left\{ \begin{array}{l} u^{(4)}(t)+{f(t,u(t),u^{'}(t),u^{''... ...}(0)=0,\quad u^{''}(1)=\alpha{u^{''}}(\eta), \end{array}\right. \end{eqnarray*}


where $0<\eta<1$, $0\leq{\alpha}<1$, $0\leq{\lambda}<1$ and $ f\in{C}({[0,1]}\times{\mathbb R}^{3},{\mathbb R})$.

Some existence results are established for this problem via upper and lower solution method and fixed point.

Received: February 19, 2011

AMS Subject Classification: 34B10, 34B15, 34B14

Key Words and Phrases: fourth-order ordinary equation, upper and lower solution method, solution existence.

Download paper from here.


Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 4