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Explicit solutions for non homogeneous Sturm-Liouville operators problems.

Lucas Jódar Sánchez (1989)

Publicacions Matemàtiques

In this paper we study existence and sufficiency conditions for the solutions of Sturm-Liouville operator problems related to the operator differential equation X'' - QX = F(t). Explicit solutions of the problem in terms of a square root of the operator Q are given.

Explicit solutions for Sturm-Liouville operator problems (II).

Lucas Jódar Sánchez (1987)

Stochastica

It is proved that the resolution problem of a Sturm-Liouville operator problem for a second-order differential operator equation with constant coefficients is solved in terms of solutions of the corresponding algebraic operator equation. Existence and uniqueness conditions for the existence of nontrivial solutions of the problem and explicit expressions of them are given.

How to state necessary optimality conditions for control problems with deviating arguments?

Lassana Samassi, Rabah Tahraoui (2008)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: inf ( u , v ) 𝒰 a d 0 1 f t , u ( θ v ( t ) ) , u ' ( t ) , v ( t ) d t , (1) where 𝒰 a d is a set of admissible controls and θ v is the solution of the following equation: { d θ ( t ) d t = g ( t , θ ( t ) , v ( t ) ) , t [ 0 , 1 ] ; θ ( 0 ) = θ 0 , θ ( t ) [ 0 , 1 ] t . (2). The results are nonlocal and new.

Indice d’un opérateur différentiel p -adique IV. Cas des systèmes. Mesure de l’irrégularité dans un disque

Philippe Robba (1985)

Annales de l'institut Fourier

Nous désirons savoir si l’opérateur différentiel d’ordre 1 , d d x + G , où G est une k × k matrice à coefficients rationnels, a un indice dans l’espace des fonctions analytiques dans une boule; dans le cas où cet indice existe nous voulons aussi le calculer. Dans le cas où k = 1 nous montrons l’existence d’un indice (si l’exposant de l’opérateur n’est pas Liouville p -adique) et nous montrons comment calculer cet indice. De même nous savons montrer l’existence d’un indice et comment calculer cet indice lorsque le système...

Integrable system of the heat kernel associated with logarithmic potentials

Kazuhiko Aomoto (2000)

Annales Polonici Mathematici

The heat kernel of a Sturm-Liouville operator with logarithmic potential can be described by using the Wiener integral associated with a real hyperplane arrangement. The heat kernel satisfies an infinite-dimensional analog of the Gauss-Manin connection (integrable system), generalizing a variational formula of Schläfli for the volume of a simplex in the space of constant curvature.

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