Page 227 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 227
TOPOLOGICAL METHODS IN DIFFERENTIAL EQUATIONS (MS-13)
[2] D. Motreanu, V. V. Motreanu, N. S. Papageorgiou, Topological and variational methods
with applications to nonlinear boundary value problems, Springer, New York, 2014.
Complex dynamics in periodically perturbed Duffing equations with
singularities
Fabio Zanolin, fabio.zanolin@uniud.it
University of Udine, Italy
Coauthor: Lakshmi Burra
We present some examples of periodically perturbed Duffing equations x + g(x) = p(t),
where g : (0, +∞) → R has a singularity at the origin: g(0+) = −∞. We prove the existence
of infinitely many subharmonic solutions, as well as the presence of chaotic-like dynamics, as
a consequence of a topological horseshoe type geometry.
An averaging method for a semilinear equation
Mirosława Zima, mzima@ur.edu.pl
University of Rzeszów, Poland
We discuss an abstract averaging method for a semilinear equation
Lx = εN (x, ε),
where L is a Fredholm mapping of index zero, and N is a nonlinear operator. The applicability
of the method for periodic solutions to n-th order differential equation and nonlocal nonlinear
boundary problems is discussed. The talk is based on a joint paper
J.A. Cid, J. Mawhin, M. Zima, An abstract averaging method with applications to differential
equations, J. Differential Equations 274 (2021), 231–250.
225
[2] D. Motreanu, V. V. Motreanu, N. S. Papageorgiou, Topological and variational methods
with applications to nonlinear boundary value problems, Springer, New York, 2014.
Complex dynamics in periodically perturbed Duffing equations with
singularities
Fabio Zanolin, fabio.zanolin@uniud.it
University of Udine, Italy
Coauthor: Lakshmi Burra
We present some examples of periodically perturbed Duffing equations x + g(x) = p(t),
where g : (0, +∞) → R has a singularity at the origin: g(0+) = −∞. We prove the existence
of infinitely many subharmonic solutions, as well as the presence of chaotic-like dynamics, as
a consequence of a topological horseshoe type geometry.
An averaging method for a semilinear equation
Mirosława Zima, mzima@ur.edu.pl
University of Rzeszów, Poland
We discuss an abstract averaging method for a semilinear equation
Lx = εN (x, ε),
where L is a Fredholm mapping of index zero, and N is a nonlinear operator. The applicability
of the method for periodic solutions to n-th order differential equation and nonlocal nonlinear
boundary problems is discussed. The talk is based on a joint paper
J.A. Cid, J. Mawhin, M. Zima, An abstract averaging method with applications to differential
equations, J. Differential Equations 274 (2021), 231–250.
225
