Related papers: Periodic Solutions with Singularities in Two Dimen…
In this work the existence of periodic solutions is studied for the Hamiltonian functions (Formula presented.) where the first term consist of a harmonic oscillator and the second term are homogeneous polynomials of degree 5 defined by two…
We present numerical results and computer assisted proofs of the existence of periodic orbits for the Kuramoto-Sivashinky equation. These two results are based on writing down the existence of periodic orbits as zeros of functionals. This…
In this paper, we prove existence results of a one-dimensional periodic solution to equations with the fractional Laplacian of order $s\in(1/2,1)$, singular nonlinearity, and gradient term under various situations, including nonlocal…
The dual Minkowski problem in the two-dimensional plane is studied in this paper. By combining the theoretical analysis and numerical estimation of an integral with parameters, we find the number of solutions to this problem for the…
In this work, we perform a first study of basic invariant sets of the spatial Hill's four-body problem, where we have used both analytical and numerical approaches. This system depends on a mass parameter mu in such a way that the classical…
Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…
A trajectory isomorphism between the two Newtonian fixed center problem in the sphere and two associated planar two fixed center problems is constructed by performing two simultaneous gnomonic projections in $S^2$. This isomorphism converts…
In this paper, we apply the Ljusternik-Schnirelman theory with local Palais-Smale condition to study a class of N-body problems with strong force potentials and fixed energies. Under suitable conditions on the potential $V$, we prove the…
A Lagrangian system with singularities is considered. The configuration space is a non-compact manifold that depends on time. A set of periodic solutions has been found.
Braids are periodic solutions to the general N-body problem in gravitational dynamics. These solutions seem special and unique, but they may result from rather usual encounters between four bodies. We aim at understanding the existence of…
The paper deals with the study of a satellite attracted by n primary bodies, which form a relative equilibrium. We use orthogonal degree to prove global bifurcation of planar and spatial periodic solutions from the equilibria of the…
In this paper, we consider periodic solutions of the $n$-body problem that satisfy symmetry constraints, expressed through invariance under finite group actions. We focus on their stability properties and present algorithms specifically…
We consider the heat equation in a multidimensional domain with nonlocal hysteresis feedback control in a boundary condition. Thermostat is our prototype model. We construct all periodic solutions with exactly two switching on the period…
Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is…
This article studies the N-vortex problem in the plane with positive vorticities. After an investigation of some properties for normalised relative equilibria of the system, we use symplectic capacity theory to show that, there exist…
Two numerical algorithms for analyzing planar central and balanced configurations in the $(n+1)$-body problem with a small mass are presented. The first one relies on a direct solution method of the $(n+1)$-body problem by using a…
A family of periodic orbits is proven to exist in the spatial lunar problem that are continuations of a family of consecutive collision orbits, perpendicular to the primary orbit plane. This family emanates from all but two energy values.…
We present mechanisms for generating conical singularities both in three and four-dimensions in the systems with copies of scalar or chiral multiplets coupled to $N=2$ or $N=1$ supergravity. Our mechanisms are useful for supersymmetry…
We proof a uniqueness and periodicity theorem for bounded solutions of uniformly elliptic equations in certain unbounded domains.
The dynamics of the 4-body problem allows for two binary collisions to occur simultaneously. It is known that in the collinear 4-body problem this simultaneous binary collision (SBC) can be block-regularised, but that the resulting block…