Convergence to equilibria in a differential equation with small delay
Convergence to equilibria in a differential equation with small delay
Consider the delay differential equation where is a constant and is Lipschitzian. It is shown that if is small, then the solutions of (1) have the same convergence properties as the solutions of the ordinary differential equation obtained from (1) by ignoring the delay.
Differentiability of perturbed semigroups and delay semigroups
Suppose that A generates a C₀-semigroup T on a Banach space X. In 1953 R. S. Phillips showed that, for each bounded operator B on X, the perturbation A+B of A generates a C₀-semigroup on X, and he considered whether certain classes of semigroups are stable under such perturbations. This study was extended in 1968 by A. Pazy who identified a condition on the resolvent of A which is sufficient for the perturbed semigroups to be immediately differentiable. However, M. Renardy showed in 1995 that immediate...
Dynamical analysis of a delayed predator-prey system with birth pulse and impulsive harvesting at different moments.
Exponential analysis of solutions of functional differential equations with unbounded terms.
First-order differential equations with several deviating arguments: Sturmian comparison method in oscillation theroy: I.
Functional differential inequalities with unbounded delay
Classical solutions of functional partial differential inequalities with initial boundary conditions are estimated by maximal solutions of suitable problems for ordinary functional differential equations. Uniqueness of solutions and continuous dependence on given functions are obtained as applications of the comparison result. A theorem on weak functional differential inequalities generated by mixed problems is proved. Our method is based on an axiomatic approach to equations with unbounded delay....
Linear functional differential equations possessing solutions with a given growth rate.
Monotone iterative techniques and a periodic boundary value problem for first-order differential equations with a functional argument.
Multiple positive solutions to singular boundary value problems for superlinear second order FDEs
We study the existence of positive solutions to the singular boundary value problem for a second-order FDE ⎧ u'' + q(t) f(t,u(w(t))) = 0, for almost all 0 < t < 1, ⎨ u(t) = ξ(t), a ≤ t ≤ 0, ⎩ u(t) = η(t), 1 ≤ t ≤ b, where q(t) may be singular at t = 0 and t = 1, f(t,u) may be superlinear at u = ∞ and singular at u = 0.
New interval oscillation criteria for second-order functional differential equations with nonlinear damping
This paper concerns the oscillation problem of second-order nonlinear damped ODE with functional terms.We give some new interval oscillation criteria which is not only based on constructing a lower solution of a Riccati type equation but also based on constructing an upper solution for corresponding Riccati type equation. We use a recently developed pointwise comparison principle between those lower and upper solutions to obtain our results. Some illustrative examples are also provided to demonstrate...
On a theorem of Haimo regarding concave mappings
A relatively simple proof is given for Haimo's theorem that a meromorphic function with suitably controlled Schwarzian derivative is a concave mapping. More easily verified conditions are found to imply Haimo's criterion, which is now shown to be sharp. It is proved that Haimo's functions map the unit disk onto the outside of an asymptotically conformal Jordan curve, thus ruling out the presence of corners.
On bounded solutions to systems of linear functional-differential equations.
On nonnegative bounded solutions to systems of linear functional differential equations.
On nonnegative solutions of nonlinear two-point boundary value problems for two-dimensional differential systems with advanced arguments.
On oscillatory fourth order nonlinear neutral differential equations. II.
On oscillatory fourth order nonlinear neutral differential equations. I.
On periodic solutions of first order nonlinear differential equations with deviating arguments.
On singular solutions of linear functional differential equations with negative coefficients.
On some qualitative behaviors of solutions to a kind of third order nonlinear delay differential equations.