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Multiple solutions of nonlinear boundary value problems for two-dimensional differential systems

Pages: 659 - 668, Issue Special, September 2009

 Abstract        Full Text (173.5K)              

Felix Sadyrbaev - Daugavpils University, Parades str. 1, LV-5400 Daugavpils, Latvia (email)
Inara Yermachenko - Daugavpils University, Parades str. 1, LV-5400 Daugavpils, Latvia (email)

Abstract: This paper discusses the quasilinearization process, that is, reduction of a given boundary value problem to a quasi-linear one. Quasi-linear BVP has a solution of definite type which is induced by oscillatory properties of the linear part of a system. Conditions are given for a solution of a modified (quasi-linear) BVP to satisfy also the original problem. It is shown that multiple quasilinearizations with different linear parts if possible lead to multiple solutions.

Keywords:  Boundary value problem, quasi-linear equation, multiple solutions
Mathematics Subject Classification:  Primary: 34B15

Received: July 2008;      Revised: March 2009;      Published: September 2009.