Multiple solutions of the BVB for two‐dimensional system by extracting linear parts and quasilinearization

Abstract

We investigate a two‐dimensional differential system of the form x^' = f (t, y), y^' = h (t, x) together with the boundary conditions x (0) = 0, x (1) = 0 by using the quasilinearization process. We show that if this problem allows for quasilinearization with respect to essentially different linear parts, then it has multiple solutions.

First Published Online: 14 Oct 2010