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Daubechies wavelets on intervals with application to BVPs

Václav Finěk (2004)

Applications of Mathematics

In this paper, Daubechies wavelets on intervals are investigated. An analytic technique for evaluating various types of integrals containing the scaling functions is proposed; they are compared with classical techniques. Finally, these results are applied to two-point boundary value problems.

De la Vallée Poussin type inequality and eigenvalue problem for generalized half-linear differential equation

Libor Báňa, Ondřej Došlý (2014)

Archivum Mathematicum

We study the generalized half-linear second order differential equation via the associated Riccati type differential equation and Prüfer transformation. We establish a de la Vallée Poussin type inequality for the distance of consecutive zeros of a nontrivial solution and this result we apply to the “classical” half-linear differential equation regarded as a perturbation of the half-linear Euler differential equation with the so-called critical oscillation constant. In the second part of the paper...

Dead cores of singular Dirichlet boundary value problems with φ -Laplacian

Ravi P. Agarwal, Donal O'Regan, Staněk, Svatoslav (2008)

Applications of Mathematics

The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem ( φ ( u ' ) ) ' = λ f ( t , u , u ' ) , u ( 0 ) = u ( T ) = A . Here λ is the positive parameter, A > 0 , f is singular at the value 0 of its first phase variable and may be singular at the value A of its first and at the value 0 of its second phase variable.

Decaying positive solutions of some quasilinear differential equations

Tadie (1998)

Commentationes Mathematicae Universitatis Carolinae

The existence of decaying positive solutions in + of the equations ( E λ ) and ( E λ 1 ) displayed below is considered. From the existence of such solutions for the subhomogeneous cases (i.e. t 1 - p F ( r , t U , t | U ' | ) 0 as t ), a super-sub-solutions method (see § 2.2) enables us to obtain existence theorems for more general cases.

Decaying Regularly Varying Solutions of Third-order Differential Equations with a Singular Nonlinearity

Ivana Kučerová (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper is concerned with asymptotic analysis of strongly decaying solutions of the third-order singular differential equation x ' ' ' + q ( t ) x - γ = 0 , by means of regularly varying functions, where γ is a positive constant and q is a positive continuous function on [ a , ) . It is shown that if q is a regularly varying function, then it is possible to establish necessary and sufficient conditions for the existence of slowly varying solutions and regularly varying solutions of (A) which decrease to 0 as t and to acquire...

Decentralized control and synchronization of time-varying complex dynamical network

Wei-Song Zhong, Jovan D. Stefanovski, Georgi M. Dimirovski, Jun Zhao (2009)

Kybernetika

A new class of controlled time-varying complex dynamical networks with similarity is investigated and a decentralized holographic-structure controller is designed to stabilize the network asymptotically at its equilibrium states. The control design is based on the similarity assumption for isolated node dynamics and the topological structure of the overall network. Network synchronization problems, both locally and globally, are considered on the ground of decentralized control approach. Each sub-controller...

Decentralized robust tracking control of uncertain large scale systems with multiple delays in the interconnections

Hansheng Wu (2009)

Kybernetika

The problem of the decentralized robust tracking and model following is considered for a class of uncertain large scale systems including time-varying delays in the interconnections. On the basis of the Razumikhin-type theorem and the Lyapunov stability theory, a class of decentralized memoryless local state feedback controllers is proposed for robust tracking of dynamical signals. It is shown that by employing the proposed decentralized robust tracking controllers, one can guarantee that the tracking...

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