Singularities of Singular Solutions of First-Order Differential Equations of Clairaut Type

2020 ◽  
Author(s):  
Kentaro Saji ◽  
Masatomo Takahashi
Keyword(s):  
Differential Equations ◽  
Singular Solutions ◽  
First Order ◽  
First Order Differential Equations

The theory of Legendrian unfoldings and first-order differential equations

1993 ◽  
Vol 123 (3) ◽  
pp. 517-532 ◽  
Author(s):  
Shyuichi Izumiya
Keyword(s):  
Differential Equations ◽  
Singular Solutions ◽  
Integrable Equations ◽  
First Order ◽  
Completely Integrable ◽  
Open Set ◽  
Complete Solutions ◽  
First Order Differential Equations

SynopsisWe consider some properties of completely integrable first-order differential equations for real-valued functions. In order to study this subject, we introduce the theory of Legendrian unfoldings. We give a characterisation of equations with classical complete solutions in terms of Legendrian unfoldings, and also assert that the set of equations with singular solutions is an open set in the space of completely integrable equations even though such a set is thin in the space of all equations.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

First-Order Differential Equations

2019 ◽  
pp. 105-153
Author(s):  
Allan Struthers ◽  
Merle Potter
Keyword(s):  
Differential Equations ◽  
First Order ◽  
First Order Differential Equations
Sign in / Sign up

Export Citation Format

Share Document