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A class of hemivariational inequalities for electroelastic contact problems with slip dependent friction
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 |
$\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.
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