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On extremal solutions of differential equations with advanced argument

100%

Augustynowicz A., Jankowski J.

Commentationes Mathematicae

2006

tom 46

nr 1

We obtain existence of absolutely continuous extremal solutions of the problem \(u'(x) = F(x, u(x), u(h(x)))\), \(u(0) = u_0\), and the Darboux problem for \(u_{xy}(x, y) = G(x, y, u(x, y), u(H(x, y)))\), where \(h\) and \(H\) are arbitrary continuous deviated arguments.

Impulsive differential equations with initial data difference

100%

Skóra L.

Commentationes Mathematicae

2011

tom 51

nr 1

In this paper, we present some results on impulsive differential inequalities and equations with initial and impulsive data difference.

Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials

86%

Karelin I., Lerer L.

International Journal of Applied Mathematics and Computer Science

2001

tom 11

nr 6

1285-1310

It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of . The proof of these results depends heavily on a new inertia theorem for matrix polynomials which is also one of the main results in this paper.

Ograniczanie wyników

2 Commentationes Mathematicae

1 International Journal of Applied Mathematics and Computer Science

1 Augustynowicz A.

1 Jankowski J.

1 Karelin I.

1 Lerer L.

1 Skóra L.

1 2011

1 2006

1 2001

Wyniki wyszukiwania

On extremal solutions of differential equations with advanced argument

Impulsive differential equations with initial data difference

Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials