相关论文: Index Theory for Zero Energy Solutions of the Plan…
The Gutzwiller's trace formula for the anisotropic Kepler problem is Fourier transformed with a convenient variable $u=1/\sqrt{-2E}$ which takes care of the scaling property of the AKP action $S(E)$. Proper symmetrization procedure…
We compute the Morse index of $1$-spike solutions of the semilinear elliptic problem \begin{equation}\label{abstr} \tag{$\mathcal P_p$} \begin{cases} -\Delta u= u^p & \text{in $\Omega$} \\ u=0 & \text{on $\partial\Omega$} \\ u>0 & \text{in…
We study positive energy solutions of the anisotropic Kepler problem with homogeneous potential. First some asymptotic property of positive energy solutions is obtained, as time goes to infinity. Afterwards, we prove the existence of…
In this paper we study the quasilinear equation $- \ep^2 \Delta u-\Delta_p u=f(u)$ in a smooth bounded domain $\Omega$ with Dirichlet boundary condition. For $\ep \geq 0$, we review existence of a least energy nodal solution and then…
In this article, the energy density of plane gravitational wave is studied by using Einstein and M{\o}ller's prescription of energy-momentum pseudotensors. The linearly polarized plan gravitational wave solution of Einstein field equation,…
An exact, plane wave solution of the gravitational field equations is investigated. The source stress tensor is represented by an anisotropic null fluid with energy flux to which the energy density $\rho$ and all pressures are finite…
The aim of the present manuscript is to develop an index theory for singular Lagrangian systems, with a particular focus on the important class of singular operators given by Bessel type differential operators. The main motivation is to…
We use Morse theory to study impulsive problems. First we consider asymptotically piecewise linear problems with superlinear impulses, and prove a new existence result for this class of problems using the saddle point theorem. Next we…
In the Newtonian $n$-body problem for solutions with arbitrary energy, which start and end either at a total collision or a parabolic/hyperbolic infinity, we prove some basic results about their Morse and Maslov indices. Moreover for…
A, recently presented, general procedure to find static and axially symmetric, interior solutions to the Einstein equations, is extended to the stationary case, and applied to find an interior solution for the Kerr metric. The solution,…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…
Morse theoretical ideas are applied to the study of relative equilibria in the planar $n$-vortex problem. For the case of positive circulations, we prove that the Morse index of a critical point of the Hamiltonian restricted to a level…
Gauge bosons associated to new gauge symmetries under which the standard model particles are not charged are predicted in many extensions of the standard model of particles and interactions. We show that under very general conditions, the…
A stationary axially symmetric solution describing a rotating anisotropic source for Einstein Field Equations(EFE) is proposed which matches to the exterior Kerr metric. The anisotropic source satisfies all energy conditions - weak, strong,…
We continue the variational approach to parabolic trajectories introduced in our previous paper [5], which sees parabolic orbits as minimal phase transitions. We deepen and complete the analysis in the planar case for homogeneous singular…
Following Smale, we study simple symmetric mechanical systems of $n$ point particles in the plane. In particular, we address the question of the linear and spectral stability properties of relative equilibria, which are special solutions of…
We study relativistic Kepler problems in the plane. At first, using non-smooth critical point theory, we show that under a general time-periodic external force of gradient type there are two infinite families of T-periodic solutions,…
Integral estimates for weak solutions to a class of Dirichlet problems for nonlinear, fully anisotropic, elliptic equations with a zero order term are obtained using symmetrization techniques.
The zero-point energy of a conducting spherical shell is studied by imposing the axial gauge via path-integral methods, with boundary conditions on the electromagnetic potential and ghost fields. The coupled modes are then found to be the…
We study a singular Hamiltonian system with an $\al$-homogeneous potential that contains, as a particular case, the classical $N$--body problem. We introduce a variational Morse--like index for a class of collision solutions and, using the…