Positive solutions for higher order multi-point boundary value problems with nonhomogeneous boundary conditions

We study nth order boundary value problems with a nonlinear term f ( t , x ) subject to nonhomogeneous multi-point boundary conditions. Criteria for the existence of positive solutions of such problems are established. Conditions are determined by the relationship between the behavior of f ( t , x ) / x near 0 and ∞ when compared with the smallest positive characteristic value of an associated linear integral operator. This work improves and extends some recent results in the literature for the second order problems. The results are illustrated with examples.