# Search Results

## You are looking at 1 - 2 of 2 items for

• Author or Editor: S. R. Grace
• Refine by Access: All Content
Clear All Modify Search

## An oscillation criterion for functional differential equations with deviating arguments

Periodica Mathematica Hungarica
Author:
S. R. Grace
An oscillation criterion is given for the differential equation
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\frac{d}{{dt}}\frac{1}{{a_{n - 1} (t)}}\frac{d}{{dt}} \ldots \frac{d}{{dt}}\frac{1}{{a_1 (t)}}\frac{d}{{dt}}x(t) + f(t,x[g_1 (t)], \ldots ,x[g_m (t)]) = 0,neven.$$ \end{document}
,n even. The obtained result is new even for the linear differential equation
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$x^{(n)} (t) + q(t)x(t) = 0,neven.$$ \end{document}
Restricted access

## Oscillations in second order differential equations with alternating coefficients

Periodica Mathematica Hungarica
Authors:
S. R. Grace
and
B. S. Lalli
Convergence of oscillatory solutions of
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$(a(t)\psi (x(t))x \cdot (t)) \cdot + p(t)x \cdot (t) + q(t)f(x(t)) = 0, \left( { \cdot = \frac{d}{{dt}}} \right)$$ \end{document}
is discussed. The results obtained extend some of the results of Graef, Kitamura, Kusano, Onose, Spikes and Singh.
Restricted access