The purpose of this work is to establish existence and location results for the higher order fully nonlinear differential equation
u⁽ⁿ⁾(t)=f(t,u(t),u′(t),…,u⁽ⁿ⁻¹⁾(t)), n≥2, with the boundary conditions
u^{(i)}(a) = A_{i}, for i=0,⋯,n-3,
u⁽ⁿ⁻¹⁾(a) = B, u⁽ⁿ⁻¹⁾(b)=C
or
u^{(i)}(a)=A_{i}, for i=0,⋯,n-3,
c₁u⁽ⁿ⁻²⁾(a)-c₂u⁽ⁿ⁻¹⁾(a)=B,
c₃u⁽ⁿ⁻²⁾(b)+c₄u⁽ⁿ⁻¹⁾(b)=C,
with A_{i},B,C ∈ R, for i=0,⋯,n-3, and c₁, c₂, c₃, c₄ real positive constants.
It is assumed that f:[a,b]×Rⁿ⁻¹→R is a continuous function satisfying one-sided Nagumo-type conditions which allows an asymmetric unbounded behaviour on the nonlinearity. The arguments are based on Leray-Schauder topological degree and lower and upper solutions method
