Displaying similar documents to “Strict ϕ disconjugacy of n -th order linear differential equations with delays”

Stability analysis for neutral stochastic systems with mixed delays

Huabin Chen, Peng Hu (2013)

Kybernetika

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This paper is concerned with the problem of the exponential stability in mean square moment for neutral stochastic systems with mixed delays, which are composed of the retarded one and the neutral one, respectively. Based on an integral inequality, a delay-dependent stability criterion for such systems is obtained in terms of linear matrix inequality (LMI) to ensure a large upper bounds of the neutral delay and the retarded delay by dividing the neutral delay interval into multiple segments....

State elimination for nonlinear neutral state-space systems

Miroslav Halás, Pavol Bisták (2014)

Kybernetika

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The problem of finding an input-output representation of a nonlinear state space system, usually referred to as the state elimination, plays an important role in certain control problems. Though, it has been shown that such a representation, at least locally, always exists for both the systems with and without delays, it might be a neutral input-output differential equation in the former case, even when one starts with a retarded system. In this paper the state elimination is therefore...

Oscillation of a logistic equation with delay and diffusion

Sheng Li Xie, Sui Sun Cheng (1995)

Annales Polonici Mathematici

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This paper establishes oscillation theorems for a class of functional parabolic equations which arises from logistic population models with delays and diffusion.

On ergodicity of some cylinder flows

Krzysztof Frączek (2000)

Fundamenta Mathematicae

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We study ergodicity of cylinder flows of the form    T f : T × ℝ → T × ℝ , T f ( x , y ) = ( x + α , y + f ( x ) ) , where f : T → ℝ is a measurable cocycle with zero integral. We show a new class of smooth ergodic cocycles. Let k be a natural number and let f be a function such that D k f is piecewise absolutely continuous (but not continuous) with zero sum of jumps. We show that if the points of discontinuity of D k f have some good properties, then T f is ergodic. Moreover, there exists ε f > 0 such that if v : T → ℝ is a function with zero integral such that D k v is of bounded...

Parametrized Cichoń's diagram and small sets

Janusz Pawlikowski, Ireneusz Recław (1995)

Fundamenta Mathematicae

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We parametrize Cichoń’s diagram and show how cardinals from Cichoń’s diagram yield classes of small sets of reals. For instance, we show that there exist subsets N and M of w w × 2 w and continuous functions e , f : w w → w w such that  • N is G δ and N x : x ∈ w w , the collection of all vertical sections of N, is a basis for the ideal of measure zero subsets of 2 w ;  • M is F σ and M x : x ∈ w w is a basis for the ideal of meager subsets of 2 w ;  • ∀ x , y N e ( x ) ⊆ N y ⇒ M x ⊆ M f ( y ) . From this we derive that for a separable metric space X,  •if for all Borel (resp. G δ ) sets...