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On Ulam Stability of a Partial Differential Operator in Banach Spaces

Author

Listed:
  • 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
    Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, P.O. Box. 68-1, 400110 Cluj-Napoca, Romania)

  • Dorian Popa

    (Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania)

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.

Suggested Citation

  • Adela Novac & Diana Otrocol & Dorian Popa, 2023. "On Ulam Stability of a Partial Differential Operator in Banach Spaces," Mathematics, MDPI, vol. 11(11), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2488-:d:1158055
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    References listed on IDEAS

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    1. Scott Carter, 2011. ""On the Cobb-Douglas and all that …": the Solow-Simon correspondence over the aggregate neoclassical production function," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 34(2), pages 255-274.
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