# American Institute of Mathematical Sciences

March  2008, 1(1): 127-137. doi: 10.3934/dcdss.2008.1.127

## Higher order two-point boundary value problems with asymmetric growth

 1 Departamento de Matemática. Universidade de Évora, Centro de Investigação em Matemática e Aplicaçoes da U.E. (CIMA-UE), Rua Romão Ramalho, 59. 7000-671 Évora, Portugal

Received  September 2006 Revised  August 2007 Published  December 2007

In this work it is studied the higher order nonlinear equation

$\u^{( n)} (x)=f(x,u(x),u^{'}(x),\ldots ,u^{( n-1)} (x))$

with $n\in \mathbb{N}$ such that $n\geq 2,$ $f:[ a,b] \times \mathbb{R}^{n}\rightarrow \mathbb{R}$ a continuous function, and the two-point boundary conditions

$u^{(i)}(a) =A_{i},\text{ \ \ }A_{i}\in \mathbb{R},\text{ \ }i=0,\ldots ,n-3$,
$u^{( n-1) }(a) =u^{( n-1) }(b)=0.$

From one-sided Nagumo-type condition, allowing that $f$ can be unbounded, it is obtained an existence and location result, that is, besides the existence, given by Leray-Schauder topological degree, some bounds on the solution and its derivatives till order $(n-2)$ are given by well ordered lower and upper solutions.
An application to a continuous model of human-spine, via beam theory, will be presented.

Citation: Feliz Minhós, A. I. Santos. Higher order two-point boundary value problems with asymmetric growth. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 127-137. doi: 10.3934/dcdss.2008.1.127
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