scholarly journals On the existence of periodic solutions for scalar second order differential equations when only the asymptotic behaviour of the potential is known

1993 ◽  
Vol 119 (2) ◽  
pp. 439-439 ◽  
Author(s):  
Alessandro Fonda
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Periodic Solutions ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Existence Of Periodic Solutions

scholarly journals Periodic solutions for periodic second-order differential equations with variable potentials

2018 ◽  
Vol 24 (2) ◽  
pp. 127-137
Author(s):  
Jaume Llibre ◽  
Ammar Makhlouf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

scholarly journals Variational Approach to Impulsive Differential Equations with Singular Nonlinearities

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Naima Daoudi-Merzagui ◽  
Abdelkader Boucherif
Keyword(s):  
Differential Equations ◽  
Variational Method ◽  
Periodic Solutions ◽  
Variational Approach ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Singular Nonlinearities ◽  
Existence Of Periodic Solutions

We discuss the existence of periodic solutions for nonautonomous second order differential equations with singular nonlinearities. Simple sufficient conditions that enable us to obtain many distinct periodic solutions are provided. Our approach is based on a variational method.

scholarly journals Periodic Solutions of Second-Order Differential Equations in Hilbert Spaces

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Alessandro Fonda ◽  
Giuliano Klun ◽  
Andrea Sfecci
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Hilbert Spaces ◽  
Second Order ◽  
Lower Upper ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Second Order Differential Equations ◽  
Existence Of Periodic Solutions ◽  
Scalar Equations

AbstractWe prove the existence of periodic solutions of some infinite-dimensional systems by the use of the lower/upper solutions method. Both the well-ordered and non-well-ordered cases are treated, thus generalizing to systems some well-established results for scalar equations.

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