相关论文: Existence and a priori bounds for electrostatic Kl…
This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves $\psi=u(x)e^{-i\omega t}$ in equilibrium with a purely electrostatic field $\mathbf{E}=-\nabla\phi(x)$. We…
This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet…
We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many static…
In this paper we consider the Klein-Gordon-Maxwell system in the electrostatic case, assuming the fall-off large-distance requirement on the gauge potential. We are interested in proving the existence of finite energy (and finite charge)…
We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many standing…
We study the class of nonlinear Klein-Gordon-Maxwell systems describing a standing wave (charged matter field) in equilibrium with a purely electrostatic field. We improve some previous existence results in the case of an homogeneous…
We consider the Klein-Gordon system posed in an inhomogeneous medium with smooth boundary subject to a local viscoelastic damping distributed around a neighborhoodof the boundary according to the Geometric Control Condition. We show that…
We prove the existence of a mountain-pass solution and the a priori bound property for the electrostatic Klein-Gordon-Maxwell equations in high dimension.
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.
We prove the existence of solutions to the conformal Einstein-scalar constraint system of equations for closed compact Riemannian manifolds in the positive case. Our results apply to the vacuum case with positive cosmological constant and…
In this article, we investigate electrostatic systems with a nonzero cosmological constant on compact manifolds with boundary. We establish new geometric properties for electrostatic manifolds in higher dimensions, extending previous…
We prove definitive results on the global stability of the flat space among solutions of the Einstein-Klein-Gordon system. Our main theorems in this monograph include: (1) A proof of global regularity (in wave coordinates) of solutions of…
Classical results concerning Klein-Gordon-Maxwell type systems are shortly reviewed and generalized to the setting of mixed local-nonlocal operators, where the nonlocal one is allowed to be nonpositive definite according to a real…
We show that, given any static spacetime whose spatial slices are asymptotically Euclidean (or, more generally, asymptotically conic) manifolds modeled on the large end of the Schwarzschild exterior, there exist stationary solutions to the…
We consider a Hamiltonian systems which is invariant under a one-parameter unitary group. We give a criterion for the stability and instability of bound states for the degenerate case. We apply our theorem to the single power nonlinear…
Let (M,g) be a smooth compact, n dimensional Riemannian manifold, n=3,4 with smooth n-1 dimensional boundary. We search the positive solutions of the singularly perturbed Klein Gordon Maxwell Proca system with homogeneous Neumann boundary…
We study the existence of cylindrically symmetric electro-magneto-static solitary waves for a system of a nonlinear Klein-Gordon equation coupled with Maxwell's equations in presence of a positive mass and of a nonnegative nonlinear…
We are interested in the problem of existence of soliton-like solutions for the nonlinear Klein-Gordon equation. In particular we study some necessary and sufficient conditions on the nonlinear term to obtain solitons of a given charge. We…
We solve the one-dimensional time-independent Klein-Gordon equation in presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker $M_{\kappa,\mu}(x)$ function, and the antiparticle bound state is…
In this paper we study the global existence and uniqueness of solution for a Klein-Gordon equations system with mixed boundary conditions. Also we analyze the asymptotic behavior of this solution.