American Institute of Mathematical Sciences

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2009, 2009(Special): 659-668. doi: 10.3934/proc.2009.2009.659

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

Felix Sadyrbaev 1, and  Inara Yermachenko 1,

1. 

Daugavpils University, Parades str. 1, LV-5400 Daugavpils

Received  July 2008 Revised  March 2009 Published  September 2009

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 .
Citation: Felix Sadyrbaev, Inara Yermachenko. Multiple solutions of nonlinear boundary value problems for two-dimensional differential systems. Conference Publications, 2009, 2009 (Special) : 659-668. doi: 10.3934/proc.2009.2009.659
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