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APPLICATIONS OF THE RETRACTION METHOD ON ANALYSIS OF EXISTENCE AND APPROXIMATION OF SOLUTIONS OF QUASILINEAR DIFFERENTIAL EQUATIONS
Pages : [1] - [10]
Received : February 19, 2014; Revised April 16, 2014
Communicated by : Professor Temur Jangveladze
Abstract
The paper presents some result on the existence and behaviour of parameter classes of solutions for system of quasilinear differential equations. Behaviour of integral curves in neighbourhoods of solution of corresponding linear system is considered. The obtained results contain the answer to the question on approximation of solutions, whose existence is established. The errors of the approximation are defined by the functions that can be sufficiently small.
The theory of qualitative analysis of differential equations and topological retraction method are used.
Keywords
quasilinear differential equation, parameter classes of solutions, behaviour of solutions, approximation of solutions.