Oscillation and nonoscillation of third order functional differential equations

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Date
1989
Authors
Tantawy, Abdalla
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R. S. Dahiya
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Mathematics
Abstract

A qualitative approach is usually concerned with the behavior of solutions of a given differential equation and usually does not seek specific explicit solutions;This dissertation is the analysis of oscillation of third order linear homogeneous functional differential equations, and oscillation and nonoscillation of third order nonlinear nonhomogeneous functional differential equations. This is done mainly in Chapters II and III. Chapter IV deals with the analysis of solutions of neutral differential equations of third order and even order. In Chapter V we study the asymptotic nature of nth order delay differential equations;Oscillatory solution is the solution which has infinitely many zeros; otherwise, it is called nonoscillatory solution;The functional differential equations under consideration are:(UNFORMATTED TABLE OR EQUATION FOLLOWS) (b(ay[superscript]')[superscript]')[superscript]' + (q[subscript]1y)[superscript]' + q[subscript]2y[superscript]' = 0, &(b(ay[superscript]')[superscript]')[superscript]' + q[subscript]1y + q[subscript]2y(t - [tau]) = 0, &(b(ay[superscript]')[superscript]')[superscript]' + qF(y(g(t))) = f(t), &(y(t) + p(t)y(t - [tau]))[superscript]''' + f(t, y(t), y(t - [sigma])) = 0, &(y(t) + p(t)y(t - [tau]))[superscript](n) + f(t, y(t), y(t - [sigma])) = 0, and &y[superscript](n) + p(t)f(t, y[tau], y[subscript]sp[sigma][subscript]1',..., y[subscript]sp[sigma][subscript]n[subscript]1(n-1)) = F(t). (TABLE/EQUATION ENDS);The first and the second equations are considered in Chapter II, where we find sufficient conditions for oscillation. We study the third equation in Chapter III and conditions have been found to ensure the required criteria. In Chapter IV, we study the oscillation behavior of the fourth and the fifth equations. Finally, the last equation has been studied in Chapter V from the point of view of asymptotic nature of its nonoscillatory solutions.

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Sun Jan 01 00:00:00 UTC 1989