Gew�hnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorr�umen

Volkmann, Peter

doi:10.1007/bf01112607

Cited by 97 publications

(29 citation statements)

References 7 publications

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“…The proof is based on the following version of comparison theorem (see, e.g., Volkmann [38] or Lemma B.3. in Filipović et al [14]): if S : R + × R → R is a continuous function which is locally Lipschitz continuous in its second variable and p, q : R + → R are differentiable functions satisfying…”

Section: Proof (I)mentioning

confidence: 99%

Stationarity and Ergodicity for an Affine Two-Factor Model

Barczy

Doering

et al. 2014

Adv. Appl. Probab.

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Section: Proof (I)mentioning

confidence: 99%

Stationarity and Ergodicity for an Affine Two-Factor Model

Barczy

Doering

et al. 2014

Adv. Appl. Probab.

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“…In nontrivial examples it may be hard to verify condition (10). In the sequel we derive an applicable sufficient condition.…”

Section: Verification Of One-sided Lipschitz Conditionsmentioning

confidence: 98%

“…), and L qmi means that £ i ->• L(t)£ is qmi (t e (a, b)) with respect to K na t which is equivalent to lij(t)> 0 (¿^¿¿€(0,6)), (see [10]). …”

Section: D+q[y -X F{t Y) -F(t X)} < L(t)q(y -X) (T € (A 6) X Y mentioning

confidence: 99%

Second Order Differential Inequalities via Aggregation

Herzog¹,

Lemmert²

2007

Demonstratio Mathematica

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Abstract. 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 Pi,---iPm, and derive monotonicity properties of solutions of second order differential inequalities under one-sided matrix Lipschitz conditions. IntroductionLet £ be a real Banach space, ordered by a cone K, that is K is a closed convex subset of E with \K C K (A > 0) and K D (-K) = {0}, and x < y :y -x € K. We will always assume that K is solid (that is Int K 0) and normal, and we write x y if y -x G Int K. Since K is solid, the set K* = {tp € E* : 0(x> 0)} is a cone, the dual cone, in the space of all continuous linear functionals E*.Throughout the paper let m > 2 and let pi,... ,p m G K \ {0} have the following properties:(1) p : = pi + h Pro £ Int K;(2) ini{pi,pj} = 0 (i^j).

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“…This definition becomes condition (Q) (Smith [14], p.78) in the cooperative case, and it generalizes, for delay systems, a related concept used by H. Schneider and M. Vidyasagar (see [17]). It can be shown to be equivalent to the monotonicity of (9) as a dynamical system in the state space of functions φ, with respect to the cone of states φ that are pointwise nonnegative, using an argument very similar to that in Theorem 5.1.1 of Smith [14] for the nontrivial direction.…”

Section: Systems With (True) Delaysmentioning

confidence: 99%

A remark on multistability for monotone systems

Enciso

Sontag

2004

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)

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Abstract-A recent paper by Angeli and Sontag presented a stability criterium for feedback loops involving single input, single output models which admit a well-defined I/O characteristic and satisfy a monotonicity condition. This paper extends the result to systems with multiple inputs and outputs and delays, and introduces a continuous-time reduction of such systems that preserves some of their stability properties.

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Gew�hnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorr�umen

Cited by 97 publications

References 7 publications

Stationarity and Ergodicity for an Affine Two-Factor Model

Stationarity and Ergodicity for an Affine Two-Factor Model

Second Order Differential Inequalities via Aggregation

A remark on multistability for monotone systems

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