%0 Journal Article %T Solvability of infinite differential systems of the form \(x' (t) =Tx(t)+b\) where \(T\) is either of the triangles \(C(\lambda)\) or \(\overline{N}_ q\) %A Fares, Ali %A Ayad, Ali %J Journal of Nonlinear Sciences and Applications %D 2012 %V 5 %N 6 %@ ISSN 2008-1901 %F Fares2012 %X In this paper, we are interested in solving infinite linear systems of differential equations of the form \(x' (t) = Tx (t) + b\) with \(x(0) = x_0\); where \(T\) is either the generalized Cesàro operator \(C (\lambda)\) or the weighted mean matrix \(\overline{N}_ q, x_0\) and b are two given infinite column matrices and \(\lambda\) is a sequence with non-zero entries. We use a new method based on Laplace transformations to solve these systems. %9 journal article %R 10.22436/jnsa.005.06.05 %U http://dx.doi.org/10.22436/jnsa.005.06.05 %P 448--458 %0 Journal Article %T An application of the infinite matrix theory to Mathieu equation %A B. de Malafosse %J Comput. Math. Appl. %D 2006 %V 52 %F Malafosse2006 %0 Journal Article %T Recent results in the infinite matrix theory and application to Hill equation %A B. de Malafosse %J Demonstratio Matematica %D 2002 %V 35 %F Malafosse2002 %0 Journal Article %T On the spectrum Cesàro operator in the space sr. Faculté des sciences de l'université d'Ankara %A B. de Malafosse %J Series Al Mathematics and statistics %D 1999 %V 48 %F Malafosse1999 %0 Journal Article %T Application of the infinite matrix theory to the solvability of a system of differential equations %A A. Farés %A A. Ayad %J J. Nonlinear Sci. Appl. %D 2012 %V 5 %F Farés2012 %0 Book %T Contribution à l'étude des opérateurs dans des espaces de suites et applications à l'optimisation et aux systèmes différentiels %A A. Farés %D 2009 %I PhD thesis, University of Le Havre %C France %F Farés2009 %0 Journal Article %T Periodic solutions of a linear differential equation of the second order %A E. L. Ince %J Proc. Cam. Philo. Soc. %D 1926 %V 23 %F Ince1926 %0 Journal Article %T On the eigenvalue problem \(-y'' + f(x)y = \lambda y\) on a semi infinite interval %A K. C-L. Issic %A P. N. Shivakumar %J Mathematical and Computer Modelling %D 2007 %V 46 %F Issic2007 %0 Journal Article %T On the spectrum of \(C_1\) as operator on bv %A J. T. Okutoyi %J Commun. Fac. Sci. Univ. Ank. Series A1 %D 1992 %V 41 %F Okutoyi 1992 %0 Book %T Sur les déterminants d'ordre infini %A H. Poincaré %D 1886 %I Bull. Soc. Math. Fr. %C 14,87 %F Poincaré1886 %0 Journal Article %T On the spectrum of the Cesàro operator %A J. B. Reade %J Bull. London Math., Soc. %D 1985 %V 17 %F Reade1985 %0 Book %T Détermination des exposants de Floquet de l'équation de Hill d'ordre n %A B. Rosseto %D 1983 %I Thèse de Doctorat d'Etat Es-Sciences %C Univ. Toulon %F Rosseto1983 %0 Journal Article %T On Hill's method in the theory of linear differential equations with periodic coefficients %A K. G. Valeev %J J. Appl. Math. Mech., transl. of Prikl. MAT. %D 1960 %V 24 %F Valeev1960