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Positive periodic solutions of N -species neutral delay systems

Hui Fang (2003)

Czechoslovak Mathematical Journal

In this paper, we employ some new techniques to study the existence of positive periodic solution of n -species neutral delay system N i ' ( t ) = N i ( t ) a i ( t ) - j = 1 n β i j ( t ) N j ( t ) - j = 1 n b i j ( t ) N j ( t - τ i j ( t ) ) - j = 1 n c i j ( t ) N j ' ( t - τ i j ( t ) ) . As a corollary, we answer an open problem proposed by Y. Kuang.

Problema di trasporto e equazione di Cauchy per campi vettoriali a variazione limitata

Luigi Ambrosio (2004)

Bollettino dell'Unione Matematica Italiana

In questa conferenza descrivo alcuni recenti sviluppi relativi al problema dell'unicità per l'equazione differenziale ordinaria e per l'equazione di continuità per campi vettoriali debolmente differenziabili. Descrivo infine un'applicazione di questi risultati a un sistema di leggi di conservazione.

Property C for ODE and Applications to an Inverse Problem for a Heat Equation

A. G. Ramm (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

Let j : = - d ² / d x ² + k ² q j ( x ) , k = const > 0, j = 1,2, 0 < e s s i n f q j ( x ) e s s s u p q j ( x ) < . Suppose that (*) 0 1 p ( x ) u ( x , k ) u ( x , k ) d x = 0 for all k > 0, where p is an arbitrary fixed bounded piecewise-analytic function on [0,1], which changes sign finitely many times, and u j solves the problem j u j = 0 , 0 ≤ x ≤ 1, u j ' ( 0 , k ) = 0 , u j ( 0 , k ) = 1 . It is proved that (*) implies p = 0. This result is applied to an inverse problem for a heat equation.

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