5 papers
Stability and Uniqueness of Slowly Oscillating Periodic Solutions to Wright's Equation
Jonathan Jaquette, Jean-Philippe Lessard, Konstantin Mischaikow
In this paper, we prove that Wright's equation has a unique slowly oscillating periodic solution (SOPS) for all parameter values ,…
Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof
Jan Bouwe van den Berg, Maxime Breden, Jean-Philippe Lessard +1
In this paper, we prove existence of symmetric homoclinic orbits for the suspension bridge equation for all parameter values . For each , a p…
A Framework for the Numerical Computation and a Posteriori Verification of Invariant Objects of Evolution Equations
Jordi-Lluís Figueras, Marcio Gameiro, Jean Philippe Lessard +1
We develop a theoretical framework for computer-assisted proofs of the existence of invariant objects in semilinear PDEs. The invariant objects considered in this paper are equilib…
Rigorous numerics for nonlinear operators with tridiagonal dominant linear part
Maxime Breden, Laurent Desvillettes, Jean-Philippe Lessard
We present a method designed for computing solutions of infinite dimensional non linear operators with a tridiagonal dominant linear part. We recast the operator equatio…
Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation
Jean-Philippe Lessard
An old conjecture in delay equations states that Wright's equation \[ y'(t)= - αy(t-1) [ 1+y(t)], α\in \mathbb{R} \] has a unique slowly oscillating periodic solution (SOPS) for ev…