2007Shuxue de shijian yu renshiRequires access

Oscillatory Criterion of a Kind of Second-order Nonlinear Variable Delay Differential Equation with Variable Coefficient

Jianguo Zhang

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Abstract

This paper studies the oscillation of second-order variable delay differential equation x(t)+p(t)f(x(g(t)))=0.By using two lemmas,we gain two sufficient conditions for the oscillation of all solutions of the equation with variable coefficient p(t).We generalize the oscillation results of second-order nonlinear differential equation and variable delay differential equation with invariable coefficient.We also develop the oscillation results of second-order nonlinear variable delay differential equation with variable coefficient.

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What this paper is about

This paper studies the oscillation of second-order variable delay differential equation x(t)+p(t)f(x(g(t)))=0.By using two lemmas,we gain two sufficient conditions for the oscillation of all solutions of the equation with variable coefficient p(t).We generalize the oscillation results of second-order nonlinear differential equation and variable delay differential equation with invariable coefficient.We also develop the oscillation results of second-order nonlinear variable delay differential equation with variable coefficient.

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Available abstract

This paper studies the oscillation of second-order variable delay differential equation x(t)+p(t)f(x(g(t)))=0.By using two lemmas,we gain two sufficient conditions for the oscillation of all solutions of the equation with variable coefficient p(t).We generalize the oscillation results of second-order nonlinear differential equation and variable delay differential equation with invariable coefficient.We also develop the oscillation results of second-order nonlinear variable delay differential equation with variable coefficient.

Key concepts: Variable (mathematics), Oscillation (cell signaling), Mathematics, Variable coefficient, Nonlinear system, Differential equation, Delay differential equation, Mathematical analysis

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