scholarly journals Oscillation criteria for a second order differential equation with a damping term

1974 ◽  
Vol 4 (2) ◽  
pp. 285-291 ◽  
Author(s):  
Manabu Naito
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Second Order ◽  
Damping Term ◽  
Oscillation Criteria ◽  
Second Order Differential Equation

Nonprincipal solutions in oscillation criteria for half-linear differential equations

2010 ◽  
Vol 47 (1) ◽  
pp. 127-137
Author(s):  
Ondřej Došlý ◽  
Jana Řezníčková
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Second Order ◽  
Oscillation Criterion ◽  
Linear Differential Equations ◽  
Integral Term ◽  
Oscillation Criteria ◽  
Second Order Differential Equation ◽  
Linear Differential

We establish a new oscillation criterion for the half-linear second order 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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$(r(t)\Phi (x'))' + c(t)\Phi (x) = 0,\Phi (x): = |x|^{p - 2} x,p > 1.$$ \end{document} In this criterion, an integral term appears which involves a nonprincipal solution of a certain equation associated with (*).

A mechanical method for the solution of second-order linear differential equations

1931 ◽  
Vol 27 (4) ◽  
pp. 546-552 ◽  
Author(s):  
E. C. Bullard ◽  
P. B. Moon
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Order Differential Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Mechanical Method ◽  
Order Linear ◽  
Second Order Differential Equation ◽  
Linear Differential

A mechanical method of integrating a second-order differential equation, with any boundary conditions, is described and its applications are discussed.

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