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In order to prove the stability theorem we exploit some uniqueness and regularity results for this class of equations that have been recently established in a companion paper [8]
Motivated by the Cauchy-Davenport theorem for sumsets, and its interpretation in terms of Cayley graphs, we prove the following main result: There is a universal constant � > 0
Section II will contain the proof of the theorem of factorization of matrix-functions and present the theorem of singular operators that are Noetherian in weighted
In the paper [2] the superstability theorem of the d’Alembert functional equation (2) appears.. The
Using this representation theorem and the deterministic characterizations of exponential stability and uniform observability obtained in [ 16 ], [ 17 ], we will prove a result of
In the first section of this paper, we give some assumptions and prelimi- naries, in section 2 and section 3, we prove the existence of an absorbing set and the existence of
The Krasnosel’skii fixed point theorem stated in that section 2 will be applied in section 3 to yield positive solutions for certain intervals of eigenvalues..
The necessary and sufficient condition in Theorem 1.1 seems stronger than that from [1, Th.3.2], but they are equivalent in our case, as we will see in Section 3.. And in Section
