Multiple Solutions of the BVB for Two‐dimensional System by Extracting Linear Parts and Quasilinearizatio

Abstract

To cite this article: I. Yermachenko (2008) 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.