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On row-finite systems of differential equations in Banach spaces

100%

Herzog G.

1998

tom Vol. 31, nr 4

835-840

We prove an existence theorem for initial value problems in Banach spaces, including a wide class of row-finite systems of ordinary differential equations.

Second order differential inequalities via aggregation

63%

Herzog G. , Lemmert R.

2007

tom Vol. 40, nr 2

347-364

Let E be a Banach space ordered by a solid and normal cone. We introduce a polynorm with respect to a given selection of positive pairwise disjoint vectors p1, . . . , pm, and derive monotonicity properties of solutions of second order differential inequalities under one-sided matrix Lipschitz conditions.

On coupled first and second order boundary value problems in ordered Banach spaces

63%

Herzog G. , Lemmert R.

2010

tom Vol. 43, nr 3

561-574

By means of a result on coupled first and second order differential inequalities and an intermediate value theorem in ordered Banach spaces, we obtain the existence of extremal solutions of boundary value problems of the form u܉ = f(t, u1, u2), u𔈀 + g(t, u1, u2) = 0, u1(a) = xa, u2(a) = ya, u2(b) = yb, between lower and upper solutions.

A note Gateaux differentials of hermitian elements in Banach algebras

63%

Herzog G. , Schmoeger C.

2008

tom Vol. 41, nr 4

909-913

Let A be a complex unital Banach algebra with unit 1. If a is an element of A is hermitian then we show that [...] and we give a proof of an inequality due to J. Nieto.

A class of hypercyclic Volterra composition operators

63%

Herzog G. , Weber A.

2006

tom Vol. 39, nr 2

465-468

We prove that certain Volterra composition operators are hypercyclic on the Frechet space of all continuous functions u : [0,1) ->- R or C with u(0) = 0.

On maximal and minimal solutions for x'(t) = F(t,x(t),x(h(t))), x(0) = x_0

63%

Herzog G. , Lemmert R.

2000

tom [Z] 40

93-102

We prove existence of maximal and minimal solutions for initial value problems for certain functional-differential equations of the form x'(t) = F(t,x(t),x(h(t))). Moreover we give conditions for these problems to be well posed. Under our conditions several forms of the case h(t) > t are included.

Banach algebra homomorphisms via orthogonal projections

63%

Herzog G. , Schmoeger C.

2006

tom Vol. 39, nr 1

137-148

Let A be a unital complex Banach algebra with unit e, and p1,... ,pn a collection of orthogonal projections with sum e. The aim of this note is to investigate the close connections of properties of a is an element of A and of (piapj) ia an element of Mn(A), where Mn(A) denotes the matrix algebra of all n x n matrices with entries in A.