Oscillation Criteria For Second Order Superlinear Differential Equations

1989 ◽  
Vol 41 (2) ◽  
pp. 321-340 ◽  
Author(s):  
CH. G. Philos
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Continuous Function ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Real Line ◽  
Nonlinear Ordinary Differential Equation ◽  
Second Order ◽  
Oscillation Criteria ◽  
Image Position

This paper is concerned with the question of oscillation of the solutions of second order superlinear ordinary differential equations with alternating coefficients.Consider the second order nonlinear ordinary differential equationwhere a is a continuous function on the interval [t0, ∞), t0 > 0, and / is a continuous function on the real line R, which is continuously differentia t e , except possibly at 0, and satisfies.

The Existence of Continuable Solutions of a Second Order Differential Equation

1977 ◽  
Vol 29 (3) ◽  
pp. 472-479 ◽  
Author(s):  
G. J. Butler
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Real Line ◽  
Order Differential Equation ◽  
Nonlinear Ordinary Differential Equation ◽  
Second Order ◽  
The Real ◽  
Second Order Differential Equation ◽  
Image Position ◽  
Sign Restriction

A much-studied equation in recent years has been the second order nonlinear ordinary differential equationwhere q and f are continuous on the real line and, in addition, f is monotone increasing with yf(y) > 0 for y ≠ 0. Although the original interest in (1) lay largely with the case that q﹛t) ≧ 0 for all large values of t, a number of papers have recently appeared in which this sign restriction is removed.

scholarly journals Oscillation Criteria for Second Order Neutral Differential Equations

1996 ◽  
Vol 48 (4) ◽  
pp. 871-886 ◽  
Author(s):  
Horng-Jaan Li ◽  
Wei-Ling Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractSome oscillation criteria are given for the second order neutral delay differential equationwhere τ and σ are nonnegative constants, . These results generalize and improve some known results about both neutral and delay differential equations.

scholarly journals Positive decreasing solutions of second order quasilinear ordinary differential equations in the framework of regular variation

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 1995-2010 ◽  
Author(s):  
Jelena Milosevic ◽  
Jelena Manojlovic
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Asymptotic Analysis ◽  
Ordinary Differential Equations ◽  
Regular Variation ◽  
Second Order ◽  
Precise Information ◽  
Varying Coefficients

This paper is concerned with asymptotic analysis of positive decreasing solutions of the secondorder quasilinear ordinary differential equation (E) (p(t)?(|x'(t)|))'=q(t)?(x(t)), with the regularly varying coefficients p, q, ?, ?. An application of the theory of regular variation gives the possibility of determining the precise information about asymptotic behavior at infinity of solutions of equation (E) such that lim t?? x(t)=0, lim t?? p(t)?(-x'(t))=?.

Qualitative properties of nonlinear ordinary differential equations

1977 ◽  
Vol 79 (1-2) ◽  
pp. 79-85 ◽  
Author(s):  
Nelson Onuchic ◽  
Plácido Z. Táboas
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Ordinary Differential Equation ◽  
Point Of View ◽  
Nonlinear Ordinary Differential Equations ◽  
Qualitative Properties ◽  
Image Position

SynopsisThe perturbed linear ordinary differential equationis considered. Adopting the same approach of Massera and Schäffer [6], Corduneanu states in [2] the existence of a set of solutions of (1) contained in a given Banach space. In this paper we investigate some topological aspects of the set and analyze some of the implications from a point of view ofstability theory.

A non-standard numerical approach to the solution of some second-order ordinary differential equations

2015 ◽  
Vol 08 (04) ◽  
pp. 1550076 ◽  
Author(s):  
A. Adesoji Obayomi ◽  
Michael Olufemi Oke
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Approach ◽  
Local Approximation ◽  
Second Order ◽  
Discrete Models ◽  
Order Ordinary Differential Equation ◽  
Non Local

In this paper, a set of non-standard discrete models were constructed for the solution of non-homogenous second-order ordinary differential equation. We applied the method of non-local approximation and renormalization of the discretization functions to some problems and the result shows that the schemes behave qualitatively like the original equation.

scholarly journals On the Modified Boundary Value Problem of De La Vallée-Poussin for Nonlinear Ordinary Differential Equations

1994 ◽  
Vol 1 (4) ◽  
pp. 429-458
Author(s):  
G. Tskhovrebadze
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Ordinary Differential Equation ◽  
Nonlinear Ordinary Differential Equations ◽  
De La Vallée Poussin

Abstract The sufficient conditions of the existence, uniqueness, and correctness of the solution of the modified boundary value problem of de la Vallée-Poussin have been found for a nonlinear ordinary differential equation u (n) = f(t, u, u′, … , u (n–1)), where the function f has nonitegrable singularities with respect to the first argument.

scholarly journals Oscillation theorems for second order superlinear differential equations with damping

1992 ◽  
Vol 53 (2) ◽  
pp. 156-165 ◽  
Author(s):  
S. R. Grace ◽  
B. S. Lalli
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Oscillation Criteria ◽  
Image Position ◽  
Oscillation Theorems

AbstractSome oscillation criteria for solutions of a general second order ordinary superlinear differential equation with alternating coefficients are given. The results generalize and complement some existing results in the literature.

OSCILLATION CRITERIA FOR CERTAIN DAMPED PDE'S WITH p-LAPLACIAN

2008 ◽  
Vol 50 (1) ◽  
pp. 129-142 ◽  
Author(s):  
ZHITING XU
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Oscillation Criteria ◽  
Image Position ◽  
Oscillation Theorems

AbstractSome oscillation criteria are obtained for the damped PDE with p-Laplacian The results established here are extensions of some classical oscillation theorems due to Fite-Wintner and Kamenev for second order ordinary differential equations, and improve and complement recent results of Mařík and Usami.

scholarly journals Quadratic approximation of solutions for ordinary differential equations

1997 ◽  
Vol 55 (1) ◽  
pp. 161-168 ◽  
Author(s):  
Juan J. Nieto
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Approximate Solutions ◽  
Nonlinear Ordinary Differential Equation ◽  
Quadratic Approximation ◽  
Monotone Sequence

We present a generalisation of the quasilinearisation method to obtain a monotone sequence of approximate solutions that converges quadratically to a solution of a nonlinear ordinary differential equation of order n ≥ 1.

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