Existence and uniqueness for an mm-point boundary value problem at resonance on infinite intervals

This paper investigates an mm-point boundary value problem with nonlinear boundary conditions at resonance on infinite intervals. By establishing a general continuation theorem, the existence and uniqueness of unbounded solutions is obtained on the basis of a suitable homotopy, Leray–Schauder degree properties and a priori estimate. This paper provides a new method to solve boundary value problems with nonlinear boundary conditions at resonance on infinite intervals.