Multiple solutions ofnonlinear boundary value problems for two-dimensional differentialsystems

Felix Sadyrbaev; Inara Yermachenko

doi:10.3934/proc.2009.2009.659

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2009, Volume 2009: 659-668. Doi: 10.3934/proc.2009.2009.659 open access

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

Felix Sadyrbaev^1, and
Inara Yermachenko¹

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

Received: June 30, 2008

Revised: February 28, 2009

Published: August 2009

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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.

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Mathematics Subject Classification: Primary: 34B15 .

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