New results in the stability study of non-autonomous evolution equations in Banach spaces

• Autorzy: Trenogin V. A. , Ion A-V.
• Języki publikacji: EN

Abstrakty

EN

The work extends some previous results of the first author, results concerning the Lyapunov stability of the zero solution of some nonautonomous nonlinear evolution equation.

Słowa kluczowe

EN

abstract evolution equations; stability

PL

algebra abstrakcyjna; równanie abstrakcyjne; stabilność

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2010
• Tom: Vol. 33
• Strony: 117--127
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Trenogin V. A.

autor

Ion A-V.

• Moscow State Steel and Alloys Institute, Russia,

Bibliografia

• [1] K. J. Engel, R. Nagel, One parameter semigroups for linear evolution equations, Springer, 2000.
• [2] G. Guhring, F. Rabiger, Linearized stability for semilinear non-autonomous evolution equations with applications to retarded di_erential equations, Ulmer Seminare, 2(1997).
• [3] A. V. Ion, Lyapunov stability of the zero solution of a perturbed abstract parabolic nonautonomous equation, ROMAI Journal, 4, 2(2008), 105-114.
• [4] R. Schnaubelt, Asymptotic behaviour of parabolic nonautonomous e quations, in Functional Evolution Equations, M. Iannelli, R. Nagel, S. Piazzera (eds.), Lecture Notes in Mathematics(1855), Springer, 2004.
• [5] V. A. Trenogin, The Lyapunov theorem on stability with respect to linear approximation as a corollary to the implicit operator theorem, Doklady Academii Nauk, 407(2006), 742-746, in Russian; English Transl. in Doklady Mathematics, 73, 2(2006), 292-295.
• [6] V. A. Trenogin, Asymptotic stability of trivial solution of differential equations with unbounded nonlinearity, in Banach spaces, ROMAI Journal, 3, 1(2007), 207-212.
• [7] V. A. Trenogin, Two reduction schemes in investigation of stability by Lyapunov and asymptotic stability for abstract parabolic differential equations, ROMAI Journal, 4, 2(2008), 169-176.