Abstract
We use some consequences of the concept of semihyperbolicity of
the solution operator to show robustness of solutions of the
linear delay differential equation
We use some consequences of the concept of semihyperbolicity of
the solution operator to show robustness of solutions of the
linear delay differential equation
A. A. Al-Nayef, Semi-hyperbolic mappings in Banach spaces, M.S. thesis, Deakin University, Australia, 1997.
View at: Google ScholarA. A. Al-Nayef, “Bi-shadowing of infinite trajectories for difference equations in Banach spaces,” Journal of Difference Equations and Applications, vol. 7, no. 4, pp. 577–585, 2001.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. A. Al-Nayef, “On the spectrum of -contracting operators,” Journal of Applied Mathematics and Stochastic Analysis, vol. 14, no. 3, pp. 303–308, 2001.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. A. Al-Nayef, P. E. Kloeden, and A. V. Pokrovskii, “Semi-hyperbolic mappings, condensing operators, and neutral delay equations,” Journal of Differential Equations, vol. 137, no. 2, pp. 320–339, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP. Diamond, P. E. Kloeden, V. S. Kozyakin, and A. V. Pokrovskii, “Robustness of the observable behavior of semihyperbolic dynamical systems,” Avtomatika i Telemekhanika, no. 11, pp. 148–159, 1995, Special issue dedicated to M. Krasnosel'skii's 75 anniversary.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP. Diamond, P. E. Kloeden, V. S. Kozyakin, and A. V. Pokrovskii, “Semihyperbolic mappings,” Journal of Nonlinear Science, vol. 5, no. 5, pp. 419–431, 1995.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetP. Diamond, P. E. Kloeden, and A. V. Pokrovskii, “Shadowing and approximation in dynamical systems,” in Miniconference on Analysis and Applications (Brisbane, 1993), G. Martin and H. B. Thompson, Eds., vol. 33 of Proc. Centre Math. Appl. Austral. Nat. Univ., pp. 47–60, Austral. Nat. Univ., Canberra, 1994.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP. Diamond, V. S. Kozyakin, P. E. Kloeden, and A. V. Pokrovskii, “Computer robustness of semi-hyperbolic mappings,” Random & Computational Dynamics, vol. 3, no. 1-2, pp. 57–70, 1995.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, vol. 99 of Applied Mathematical Sciences, Springer, New York, 1993.
View at: Google Scholar | Zentralblatt MATH | MathSciNetY. Hino, S. Murakami, and T. Naito, Functional-Differential Equations with Infinite Delay, vol. 1473 of Lecture Notes in Mathematics, Springer, Berlin, 1991.
View at: Google Scholar | Zentralblatt MATH | MathSciNetB. Lani-Wayda, Hyperbolic Sets, Shadowing and Persistence for Noninvertible Mappings in Banach Spaces, vol. 334 of Pitman Research Notes in Mathematics Series, Longman, Harlow, 1995.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Yu. Pilyugin, The Space of Dynamical Systems with the -Topology, vol. 1571 of Lecture Notes in Mathematics, Springer, Berlin, 1994.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. K. Rabaa, Semi-hyperbolicity and differential equations with infinite delay, Master's thesis, Mu'tah University, Jordan, 2003.
View at: Google Scholar