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3 Demonstratio Mathematica

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Inequalities and means from a cyclic differential equation

Herzog G., Kunstmann P.

Demonstratio Mathematica

2014

Vol. 47, nr 2

300--309

We prove that the solution of the cyclic initial value problem (…) is convergent to an equilibrium (…) , and study the properties of the function (…) and its relation to Shapiro’s inequality.

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

Herzog G., Lemmert R.

Demonstratio Mathematica

2010

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.

On Riccati equation in ordered Banach algebras

Herzog G., Lemmert R.

Demonstratio Mathematica

2002

Vol. 35, nr 4

783-790

We consider Riccati differential equations in ordered Banach algebras A, and prove invariance and comparison theorems for the case that the right hand side of a Riccati equation is quasimonotone increasing on the set of quasipositive elements (which are the quasimonotone increasing linear mappings in case that A is the operator algebra of an ordered Banach space).