Funkcialaj Ekvacioj, 43 (2000) 39-56

Weak Hyperbolicity of Delay Differential Equations and the 3/2-Type Stability Conditions

Sergei I. TROFIMCHUK and Anatoli F. IVANOV
Universidad de Chile, Chile and Pennsylvania State University, USA

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References

• Busenberg, S. and Cooke, K., Stability conditions for linear nonautonomous delay differential equations, Quart. Appl. Math., 42 (1984), no. 3, 295-306.
• Dunford, N. and Schwartz, J. T., Linear Operators, vol. 1, Interscience Publishers, Inc., New York, 1958.
• Gopalsamy, K., Stability and oscillations in delay differential equations of population dynamics, Mathematics and its Applications, 74. Kluwer, 1992.
• Gopalsamy, K. and Trofimchuk, S., Almost periodic solution of Lasota-Wazewska type delay differential equation, J. Math. Anal. Appl., 237 (1999), 106-127.
• Hale, J. K. and verdun Lunel, S. M., Introduction to Functional Differential Equations. Springer-Verlag, 1993.
• Kolmanovskii, V. and Myshkis, A., Applied theory of functional differential equations, Mathematics and its Applications, 85. Kluwer, 1992.
• Krisztin., T., On stability properties for one-dimensional functional differential equations, Funkcial. Ekvac., 34 (1991), 241-256.
• Ladas, G., Sficas, Y. G. and Stavroulakis, I. P., Asymptotic behavior of solutions of retarded differential equations, Proc. Amer. Math. Soc. 88, 2 (1983), 247-253.
• Latushkin, Y. and Montgomery-Smith, S. and Randolph, T., Evolutionary semigroups and dichotomy of linear skew-product flows on locally compact spaces with banach fibers. J. Differential Equations, 125 (1996), 73-116.
• Malygina, V. V., Some criteria for stability equations with a lagging argument, Differents. Uravn., 28, 10 (1992), 1716-1723.
• Sacker, R. J. and Sell, R. A., A spectral theory for linear differential systems. J. Differential Equations, 27 (1978), no. 3, 320-358.
• Sacker, R. J. and Sell, R. A., Dichotomies for linear evolutionary equations in Banach spaces. J. Differential, Equations, 113 (1994), no. 1, 17-67.
• Sell, G. R., Topological dynamics and ordinary differential equations, Van Nostrand Reinhold Mathematical Studies, No. 33. Van Nostrand Reinhold Co., London, 1971.
• So, J. W.-H., Yu J. S. and Chen, Ming-Po., Asymptotic stability for scalar delay differential equations, Funkcial. Ekvac., 39 (1996), l-17.
• Yoneyama, T., On the 3/2 stability theorem for one-dimensional delay-differential equations, J. Math. Anal. Appl., 125 (1987), 161-173.
• Yorke, J. A., Asymptotic stability for one-dimensional differential delay equations, J. Differential Equations, 7 (1970), 189-202.
• Ivanov, A., Liz, E. and Trofwchuk, S., Halanay inequality, Yorke 3/2 stability criterion and differential equations with maxima, SITMS Research Report No. 40/99, 1999, submitted.