9 papers · 1 filter
A novel 2+1-dimensional extended Dym equation: moving boundary problems solvable via Painlevé II symmetry reduction
Colin Rogers, Pablo Amster
A novel 2+1-dimensional extension of the solitonic Dym equation is shown to admit a Painlevé II symmetry reduction which permits the exact solution of a class of Stefan-type moving…
A discretisation of the Ermakov-Painlevé II equation: Dirichlet and Robin-type boundary value problems
Pablo Amster, Colin Rogers
Two-point boundary value problems for a discrete Ermakov-Painlevé II equation are analysed by means of topological methods. In addition, an alternative variational approach is deta…
On an affinity principle by Krasnoselskii
Pablo Amster, Julián Epstein
An abstract formulation of a duality principle established by Krasnoselskii is presented. Under appropriate conditions, it shall be shown that, if the solutions of a nonlinear func…
On Landesman-Lazer conditions and the Fundamental Theorem of Algebra
Pablo Amster
We give an elementary proof of a Landesman-Lazer type result for systems by means of a shooting argument and explore its connection with the fundamental theorem of algebra.
Systems of functional-differential equations periodic solutions for systems of functional-differential semilinear equations at resonance
Pablo Amster, Julián Epstein, Arturo Sanjuán
Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional…
Persistence and periodic solutions in systems of delay differential equations
Pablo Amster, Melanie Bondorevsky
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to gua…