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2011 Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems
A. Boichuk, J. Diblík, D. Khusainov, M. Růžičková
Abstr. Appl. Anal. 2011(SI1): 1-19 (2011). DOI: 10.1155/2011/631412


Conditions are derived of the existence of solutions of nonlinear boundary-value problems for systems of n ordinary differential equations with constant coefficients and single delay (in the linear part) and with a finite number of measurable delays of argument in nonlinearity: z˙(t)=Az(t-τ)+g(t)+ϵZ(z(hi(t),t,ϵ), t[a,b], assuming that these solutions satisfy the initial and boundary conditions z(s):=ψ(s) if s[a,b], lz()=αm. The use of a delayed matrix exponential and a method of pseudoinverse by Moore-Penrose matrices led to an explicit and analytical form of sufficient conditions for the existence of solutions in a given space and, moreover, to the construction of an iterative process for finding the solutions of such problems in a general case when the number of boundary conditions (defined by a linear vector functional 𝓁) does not coincide with the number of unknowns in the differential system with a single delay.


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A. Boichuk. J. Diblík. D. Khusainov. M. Růžičková. "Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems." Abstr. Appl. Anal. 2011 (SI1) 1 - 19, 2011.


Published: 2011
First available in Project Euclid: 12 August 2011

zbMATH: 1222.34075
MathSciNet: MR2802836
Digital Object Identifier: 10.1155/2011/631412

Rights: Copyright © 2011 Hindawi

Vol.2011 • No. SI1 • 2011
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