Results 301 to 310 of about 683,225 (336)

On the oscillation of functional differential equations

Mathematische Nachrichten, 1999
AbstractIn this paper we present certain criteria for the oscillation of functional differential equations of the form where δ = ±1, p, g: [t0, ∞) → IR, H: [t0,∞) × IR → IR are continuous, p(t) ≥ 0 for t ≥ t0 and limt → ∞ g(t) — ∞. We like to point out that condition of the form will not be employed.
S. R. Grace, G. G. Hamedani
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Functional Differential Equations

2019
Equations determining a functional and involving variational derivatives are called functional differential equations (abbreviated by fde, list in Chap. 1). Definitions and elementary properties of such equations are discussed to prepare the subsequent development on fdes. Two types of such equations are considered: elliptic and parabolic fdes.
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Functional — Differential Equations

2003
In this chapter we consider one more class of problems the solution of which can be obtained by the parametric continuation method. This is the initial value problem (the Cauchy problem) for the functional differential equations. The equations with nonlocal retarded argument and integro differential equations can be included into this class of problems.
E. B. Kuznetsov, V. I. Shalashilin
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On a Functional Differential Equation

IMA Journal of Applied Mathematics, 1971
D. F. Mayers, John Ockendon, L. Fox, A. B. Tayler   +3 more
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Functional Differential Equations

2018
The goal of this chapter is to apply the theories developed in the previous chapters to functional differential equations. In Section 7.1 retarded functional differential equations are rewritten as abstract Cauchy problems and the integrated semigroup theory is used to study the existence of integrated solutions and to establish a general Hopf ...
Shigui Ruan, Pierre Magal
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Coerciveness of functional-differential equations

Mathematical Notes, 1996
The author considers functional-differential equations with Dirichlet conditions and with contraction and dilatation of the arguments. Necessary and sufficient conditions are obtained under which a Gårding type inequality holds.
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Boundedness in functional differential equations

Nonlinear Analysis: Theory, Methods & Applications, 1994
The uniform boundedness and the uniform ultimate boundedness of solutions \(x(t)\) to the system of functional differential equations \(x'(t) = F(t,x_ t)\), \(x \in R^ n\) are considered. Both cases of systems with finite and infinite delay are developed. New Lyapunov-type theorems which generalized previous results of Yoshizawa, Burton/Zhang, Hale and
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Remarks on a functional differential equation

Annalen der Physik, 2003
AbstractIn this paper we shall study the functional differential equation . After recapitulating some known results we give some estimates and show the results of numerical calculations.
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Functional Differential Equations

1981
A distinguishing feature of ordinary differential equations is that the future behavior of solutions depends only upon the present (initial) values of the solution. Numerous physical, economic, biological, and social systems, though, exhibit hereditary dependence. That is, the future state of the system depends not only upon the present state, but also
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Functional Differential Equations

1968
Lyapunov’s second method gives sufficient conditions for stability and asymptotic stability. This method has been extended in several directions.7,8 One of the interesting extension of this method depends basically on the fact that a function satisfying the inequality $$m'(t)\leq w(t,m(t)) \;\;\;\;\;\;\; m(t_{0})=r_{0}$$ is majorized by the ...
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