scholarly journals Periodic Solutions in Slowly Varying Discontinuous Differential Equations: The Generic Case

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2449
Author(s):  
Flaviano Battelli ◽  
Michal Fečkan
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Singularly Perturbed ◽  
Two Dimensional ◽  
Singularly Perturbed Equation ◽  
Discontinuous Differential Equations ◽  
Scalar Variable ◽  
Perturbed Equation

We study persistence of periodic solutions of perturbed slowly varying discontinuous differential equations assuming that the unperturbed (frozen) equation has a non singular periodic solution. The results of this paper are motivated by a result of Holmes and Wiggins where the authors considered a two dimensional Hamiltonian family of smooth systems depending on a scalar variable which is the solution of a singularly perturbed equation.

scholarly journals Multiplicity of positive periodic solutions to second order differential equations

2006 ◽  
Vol 73 (2) ◽  
pp. 175-182 ◽  
Author(s):  
Jifeng Chu ◽  
Xiaoning Lin ◽  
Daqing Jiang ◽  
Donal O'Regan ◽  
R. P. Agarwal
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Positive Periodic Solution ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Second Order Differential Equations

In this paper, we study the existence of positive periodic solutions to the equation x″ = f (t, x). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.

On the existence of periodic solutions for autonomous retarded functional differential equations on R2

1986 ◽  
Vol 102 (3-4) ◽  
pp. 259-262 ◽  
Author(s):  
J. G. Dos Reis ◽  
R. L. S. Baroni
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Retarded Functional Differential Equations ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

SynopsisLet Ca be the set of all the continuous functions from the interval [−r, 0] on the sphere of radius a, on the plane. We prove, under certains conditions, that a retarded autonomous differential equation that leaves Ca invariant has a non-constant periodic solution.

T-periodic solutions for some second order differential equations with singularities

1992 ◽  
Vol 120 (3-4) ◽  
pp. 231-243 ◽  
Author(s):  
Manuel del Pino ◽  
Raúl Manásevich ◽  
Alberto Montero
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Positive Solutions ◽  
Resonance Condition ◽  
Second Order ◽  
Fredholm Alternative ◽  
Positive Slope ◽  
Second Order Differential Equations ◽  
Image Position

SynopsisWe study the existence of T-periodic positive solutions of the equationwhere f(t, .) has a singularity of repulsive type near the origin. Under the assumption that f(t, x) lies between two lines of positive slope for large and positive x, we find a non-resonance condition which predicts the existence of one T-periodic solution.Our main result gives a Fredholm alternative-like result for the existence of T-periodic positive solutions for

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