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.

Key words:

• quasilinearization
• quasi‐linear system
• i‐nonresonant linear part
• i‐type solution
• Green's matrix

Notes

The work was advised by prof. F. Sadyrbaev (Institute of Mathematics and Computer Science, University of Latvia).