Higher order two-point boundary value problems with asymmetric growth

Abstract

In this work it is studied the higher order diferential equation

u^(n)(t)=f(t,u(t),u′(t),...,u^(n-1)(t))

with n∈N such that n≥2, t∈[a,b], f:[a,b]×Rⁿ→R a continuous function and the two-point boundary conditions

u^{(i)}(a)=A_{i}, A_{i}∈R, i=0,...,n-3.

u^(n-1)(a)=0, u^(n-1)(b)=0.

From one-sided Nagumo type conditions, 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 of the solution and its derivatives till (n-2) are given by the well order lower and upper solutions. An application to a continuous model of human-spine, via beam theory, will be presented.