On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays

This article is concerned with solutions that behave asymptotically like polynomials for nth order ( n > 1 ) nonlinear ordinary differential equations. For each given integer m with 1 ⩽ m ⩽ n - 1 , sufficient conditions are presented in order that, for any real polynomial of degree at most m, there exists a solution which is asymptotic at ∞ to this polynomial. Conditions are also given, which are sufficient for every solution to be asymptotic at ∞ to a real polynomial of degree at most n - 1 . The application of the results obtained to the special case of second order nonlinear differential equations leads to improved versions of the ones contained in the recent paper by Lipovan [Glasg. Math. J. 45 (2003) 179] and of other related results existing in the literature.

Asymptotic to polynomials solutions for nonlinear differential equations

On considere des equations de la forme: L n x(t)+σ Σ h=1 N q h (t). x(g h (t))=0, L n x(t)+σ∑ h=1 N q h (t)f h (x(g h (t)))=0 ou L n est un operateur differentiel disconjugue defini par recurrence par L 0 x=x, L i x=1/p i •dl i-1 x/dt (1≤i≤n), p n ≡1

/pdf/oscillation-of-functional-differential-equations-with-2etjjwvvbc.pdf

Oscillation of functional-differential equations with general deviating arguments

This paper is dealing with the oscillatory and asymptotic behavior of the bounded solutions of n-th order (n>1) differential equations with deviating arguments involving the so called r-derivatives Dr(i)x (i=0, 1, ..., n) of the unknown function x defined by
Open image in new window
, where ri (i=1, 2, ..., n−1) are positive continuous functions on the interval [t0, ∞). The fundamental purpose is to find a necessary and sufficient condition in order to have at least one (bounded nonoscillatory) solution whose the limit at ∞ exists inR−{0}.

/pdf/oscillatory-and-asymptotic-behavior-of-the-bounded-solutions-51iexkcv59.pdf

Oscillatory and asymptotic behavior of the bounded solutions of differential equations with deviating arguments

Some Oscillation Problems for a Second Order Linear Delay Differential Equation

/pdf/asymptotic-properties-of-nonoscillatory-solutions-of-21nurdjmjc.pdf

Asymptotic properties of nonoscillatory solutions of differential equations with deviating argument

/pdf/on-the-asymptotic-behavior-of-nonoscillatory-solutions-of-k41s3ehg33.pdf

Ch. G. Philos

Papers

Oscillatory and asymptotic behavior of the bounded solutions of differential equations with deviating arguments

Asymptotic properties of nonoscillatory solutions of differential equations with deviating argument

On the asymptotic behavior of nonoscillatory solutions of differential equations with deviating arguments