Aronszajn-Smith conditions for open sets. (Conditions d'Aronszajn-Smith pour les ouverts de classe .)
Moukaddem, N. (2001)
Rendiconti del Seminario Matematico
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Moukaddem, N. (2001)
Rendiconti del Seminario Matematico
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Buşe, Constantin (2003)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Phóng Vũ (1999)
Studia Mathematica
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A characterization of exponentially dichotomic and exponentially stable -semigroups in terms of solutions of an operator equation of Lyapunov type is presented. As a corollary a new and shorter proof of van Neerven’s recent characterization of exponential stability in terms of boundedness of convolutions of a semigroup with almost periodic functions is given.
Megan, M., Sasu, L., Sasu, B. (2000)
Acta Mathematica Universitatis Comenianae. New Series
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Vũ Phóng (1997)
Banach Center Publications
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This paper is chiefly a survey of results obtained in recent years on the asymptotic behaviour of semigroups of bounded linear operators on a Banach space. From our general point of view, discrete families of operators on a Banach space X (discrete one-parameter semigroups), one-parameter -semigroups on X (strongly continuous one-parameter semigroups), are particular cases of representations of topological abelian semigroups. Namely, given a topological abelian semigroup S, a family...
Ungureanu, Viorica Mariela (2004)
Acta Universitatis Apulensis. Mathematics - Informatics
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Cheban, D.N. (2001)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Buşe, Constantin, Jitianu, Oprea (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Aulbach, Bernd, Nguyen Van Minh (1998)
Abstract and Applied Analysis
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Nguyen Thieu Huy, Ngo Quy Dang (2016)
Annales Polonici Mathematici
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We prove the existence and conditional stability of periodic solutions to semilinear evolution equations of the form u̇ = A(t)u + g(t,u(t)), where the operator-valued function t ↦ A(t) is 1-periodic, and the operator g(t,x) is 1-periodic with respect to t for each fixed x and satisfies the φ-Lipschitz condition ||g(t,x₁) - g(t,x₂)|| ≤ φ(t)||x₁-x₂|| for φ(t) being a real and positive function which belongs to an admissible function space. We then apply the results to study the existence,...
Buse, C., Zada, A. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Ahmed, N.U. (1994)
Journal of Applied Mathematics and Stochastic Analysis
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