Asymptotic behavior and oscillation of functional differential equations

Asymptotic relations between the solutions of a linear autonomous functional differential equation and the solutions of the corresponding perturbed equation are established. In the scalar case, it is shown that the existence of a nonoscillatory solution of the perturbed equation often implies the existence of a real eigenvalue of the limiting equation. The proofs are based on a recent Perron type theorem for functional differential equations.

[1]  J. Mallet-Paret.  Morse Decompositions for delay-differential equations , 1988 .

[2]  M. Pituk.  The Hartman-Wintner Theorem for Functional Differential Equations , 1999 .

[3]  John Mallet-Paret,et al.  The Global Structure of Traveling Waves in Spatially Discrete Dynamical Systems , 1999 .

[4]  John Mallet-Paret,et al.  The Fredholm Alternative for Functional Differential Equations of Mixed Type , 1999 .

[5]  Bingtuan Li,et al.  Oscillations of Delay Differential Equations with Variable Coefficients , 1995 .

[6]  F. Kappel,et al.  An elementary divisor theory for autonomous linear functional differential equations , 1976 .

[7]  Á. Elbert,et al.  Oscillation and nonoscillation criteria for delay differential equations , 1995 .

[8]  Ovide Arino,et al.  The Two-Dimensional Attractor of a Differential Equation with State-Dependent Delay , 2001 .

[9]  Yulin Cao,et al.  The discrete Lyapunov function for scalar differential delay equations , 1990 .

[10]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[11]  M. Pituk.  A Perron type theorem for functional differential equations , 2006 .

[12]  G. Ladas,et al.  On oscillation of nonlinear delay differential equations , 1987 .

[13]  S. Lunel,et al.  Delay Equations. Functional-, Complex-, and Nonlinear Analysis , 1995 .

[14]  F. V. Vleck,et al.  Stability and Asymptotic Behavior of Differential Equations , 1965 .

[15]  G. Ladas,et al.  Oscillation Theory of Delay Differential Equations: With Applications , 1992 .

[16]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[17]  István Györi,et al.  On the existence of rapidly oscillatory solutions in the Nicholson blowflies equation , 2002 .