Related papers: Periodic solutions for the N-vortex problem via a …
In this study, we focus on the existence of a periodic solution for the neutral nonlinear dynamic systems with delay% \[ x^{\Delta}(t)=A(t)x(t)+Q^{\Delta}\left(t,x\left(\delta_{-}(s,t)\right) \right)…
In this paper, we first describe how we can arrange any bodies on Figure-Eight without collision in a dense subset of $[0,T]$ after showing that the self-intersections of Figure-Eight will not happen in this subset. Then it is reasonable…
The restricted three-vortex problem is investigated with one of the point vortices fixed in the plane. The motion of the free vortex having zero circulation is explored from a rotating frame of reference within which the free vortex with…
We consider equations of the form $ u_t = \nabla \cdot ( \gamma(u) \nabla \mathrm{N}(u))$, where $\mathrm{N}$ is the Newtonian potential (inverse of the Laplacian) posed in the whole space $\mathbb R^d$, and $\gamma(u)$ is the mobility. For…
Existence, uniqueness, and regularity of time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space are investigated. We consider the Navier-Stokes equations with a non-zero drift term corresponding to the…
We present a series of existence theorems for multiple vortex solutions in the Gudnason model of the ${\cal N}=2$ supersymmetric field theory where non-Abelian gauge fields are governed by the pure Chern--Simons dynamics at dual levels and…
We consider generic differential equations in $\mathbb{R}$ with a finite number of hyperbolic equilibria, which are subject to $\omega$--periodic instantaneous perturbative pulses ($\omega>0$). Using the time-$ \omega$ map of the original…
Vortices in non-Abelian gauge field theory play important roles in confinement mechanism and are governed by systems of nonlinear elliptic equations of complicated structures. In this paper, we present a series of existence and uniqueness…
In this tutorial we address the existence and stability of periodic and quasiperiodic orbits in N degree of freedom Hamiltonian systems and their connection with discrete symmetries. Of primary importance in our study are the nonlinear…
This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $\alpha$ and $\beta$ violate the boundary conditions $…
We consider compact binary systems, modeled in general relativity as vacuum or perfect-fluid spacetimes with a helical Killing vector k^\alpha, heuristically, the generator of time-translations in a corotating frame. Systems that are…
A central focus of Ginzburg-Landau theory is the understanding and characterization of vortex configurations. On a bounded domain $\Omega\subseteq \mathbb{R}^2,$ global minimizers, and critical states in general, of the corresponding energy…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
We investigate the presence of vortex structures in generalized Maxwell-Higgs and Chern-Simons-Higgs models in the three-dimensional spacetime. Despite the important difference between the Maxwell and Chern-Simons dynamics, we have been…
The motion of point vortices constitutes an especially simple class of solutions to Euler's equation for two dimensional, inviscid, incompressible, and irrotational fluids. In addition to their intrinsic mathematical importance, these…
In this work we study a nonlinear Volterra equation with non-symmetric feedback that arises as a particular case of the Gurtin-MacCamy model in population dynamics. We are particularly interested in the existence of slowly oscillating…
We try to generalize a result of M. Willem on forced periodic oscillations which required the assumption that the forced potential is periodic on spatial variables. In this paper, we only assume its integral on the time variable is…
We study periodic solutions of a one-degree of freedom micro-electro-mechanical system (MEMS) with a parallel-plate capacitor under $T$--periodic electrostatic forcing. We obtain analytical results concerning the existence of $T-$ periodic…
We study the generalized point-vortex problem and the Gross-Pitaevskii equation on surfaces of revolution. We find rotating periodic solutions to the generalized point-vortex problem, which have two two rings of $n$ equally spaced vortices…
The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our…