On Ulam Stability of a Partial Differential Operator in Banach Spaces

Adela Novac, Diana Otrocol () and Dorian Popa
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Adela Novac: Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
Diana Otrocol: Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
Dorian Popa: Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania

Mathematics, 2023, vol. 11, issue 11, 1-10

Abstract: In this paper, we prove that, if inf x ∈ A | f ( x ) | = m > 0 , then the partial differential operator D defined by D ( u ) = ∑ k = 1 n f k ∂ u ∂ x k − f u , where f , f i ∈ C ( A , R ) , u ∈ C 1 ( A , X ) , i = 1 , … , n , I ⊂ R is an interval, A = I × R n − 1 and X is a Banach space, is Ulam stable with the Ulam constant K = 1 m . Moreover, if inf x ∈ A | f ( x ) | = 0 , we prove that D is not generally Ulam stable.

Keywords: Ulam stability; partial differential operator; gauge; Banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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