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

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

Keyword : quasilinearization, quasi-linear system, i-nonresonant linear part, itype solution, Green’s matrix

How to Cite
Yermachenko, I. (2008). Multiple solutions of the BVB for two‐dimensional system by extracting linear parts and quasilinearizatio. Mathematical Modelling and Analysis, 13(2), 303-312. https://doi.org/10.3846/1392-6292.2008.13.303-312
Published in Issue
Jun 30, 2008
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