On a problem concerning a functional-differential equation

Kristína Smítalová

Displaying similar documents to “On a problem concerning a functional-differential equation”

Sets of determination for solutions of the Helmholtz equation

Jarmila Ranošová (1997)

Commentationes Mathematicae Universitatis Carolinae

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Let $α > 0$ , $λ = {(2 α)}^{- 1 / 2}$ , $S^{n - 1}$ be the $(n - 1)$ -dimensional unit sphere, $σ$ be the surface measure on $S^{n - 1}$ and $h (x) = \int_{S^{n - 1}} e^{λ 〈 x, y 〉} d σ (y)$ . We characterize all subsets $M$ of $ℝ^{n}$ such that $inf_{x \in ℝ^{n}} \frac{u (x)}{h (x)} = inf_{x \in M} \frac{u (x)}{h (x)}$ for every positive solution $u$ of the Helmholtz equation on $ℝ^{n}$ . A closely related problem of representing functions of $L_{1} (S^{n - 1})$ as sums of blocks of the form $e^{λ 〈 x_{k}, . 〉} / h (x_{k})$ corresponding to points of $M$ is also considered. The results provide a counterpart to results for classical harmonic functions in a ball, and for parabolic functions on a slab, see References.

A nonintersection property for extremals of variational problems with vector-valued functions

Alexander J. Zaslavski (2006)

Annales de l'I.H.P. Analyse non linéaire

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General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations

N. Dilna, A. Rontó (2008)

Mathematica Bohemica

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New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order.