On solvability of linear differential equations in Rn

• Autorzy: Shkarin S. A.
• Języki publikacji: EN

Abstrakty

EN

We construct xo is an element of RN and a row-finite matrix T = {Ti,j(t)}i,j is an element of N of polynomials of one real variable t such that the Cauchy problem x(t) = Ttx(t), x{0) = xo in the Frechet space RN has no solutions. We also construct a row-finite matrix A = {Aij(t)}ij is an element of N of C°°(R) functions such that the Cauchy problem x{t) = Atx;(t), x(0) = xo in RN has no solutions for any xo infinity RN\ {0}. We provide some sufficient condition of solvability and unique solvability for linear ordinary differential equations x(t) = Ttx(t) with matrix elements Ti,j(t) analytically dependent on t.

Słowa kluczowe

EN

Cauchy problem; Frechet space; linear differential equations

PL

problem Cauchy'ego; funkcje różniczkowe; przestrzeń Frecheta

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 1
• Strony: 85--99
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Shkarin S. A.

• Department of Mathematical, Analysis University of Seville, C/Tarfia, S/N, C.P. 41012 Seville, Spain

Bibliografia

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