scholarly journals Factorization method for some inhomogeneous Lienard equations

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 443
Author(s):  
O. Cornejo Perez ◽  
S. C. Mancas ◽  
H. C. Rosu ◽  
C. A. Rico-Olvera
Keyword(s):  
Differential Equations ◽  
Closed Form ◽  
Factorization Method ◽  
Closed Form Solutions ◽  
First Order ◽  
Liénard Equations ◽  
First Order Differential Equations

The factorization of inhomogeneous Li\'enard equations is performed showing that through the factorization conditions involved in the method one can obtain forcing terms for which closed-form solutions exist. Because of the reduction of order feature of factorization, the solutions are simultaneously solutions of first-order differential equations with polynomial nonlinearities. Several illustrative examples of such solutions are presented, generically having rational parts and consequently singularities.

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.

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