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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.

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.

Déterminants et intégrales de Fresnel

Yves Colin de Verdière (1999)

Annales de l'institut Fourier

On présente ici une approche directe et géométrique pour le calcul des déterminants d’opérateurs de type Schrödinger sur un graphe fini. Du calcul de l’intégrale de Fresnel associée, on déduit le déterminant. Le calcul des intégrales de Fresnel est grandement facilité par l’utilisation simultanée du théorème de Fubini et d’une version linéaire du calcul symbolique des opérateurs intégraux de Fourier. On obtient de façon directe une formule générale exprimant le déterminant en terme des conditions...

Determination of the diffusion operator on an interval

Ibrahim M. Nabiev (2014)

Colloquium Mathematicae

The inverse problem of spectral analysis for the diffusion operator with quasiperiodic boundary conditions is considered. A uniqueness theorem is proved, a solution algorithm is presented, and sufficient conditions for the solvability of the inverse problem are obtained.

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