The numerical solution of the bi-dimensional nonlinear Poisson equations under Cauchy boundary conditions is considered. Using Green identity we show that this problem is equivalent to solve a bi-dimensional Fredholm ...

This paper is concerned with both the local and global internal controllability of the 1D Schroedinger-Poisson equation i u_t =  -u_xx +V (u) u; which arises in quantum semiconductor models. Here V (u) is a Hartree-type ...

In this article we study the existence and concentration behavior of bound states for a nonlinear Schrodinger-Poisson system with a parameter epsilon > 0. Under suitable conditions on the potential functions, we prove that ...

This paper is concerned with the internal distributed control problem for the 1D Schrödinger equation, i ut(x,t) = −uxx+α(x) u+m(u) u, that arises in quantum semiconductor models. Here m(u) is a non local Hartree–type ...

A method to construct Hamiltonian theories for systems of both ordinary and partial differential equations is presented. The knowledge of a Lagrangian is not at all necessary to achieve the result. The only ingredients ...

The Poisson-Boltzmann equation (PBE), with specific ion-surface interactions and a cell model, was used to calculate the electrostatic properties of aqueous solutions containing vesicles of ionic amphiphiles. Vesicles are ...

The Poisson-Boltzmann equation (PBE), with specific ion-surface interactions and a cell model, was used to calculate the electrostatic properties of aqueous solutions containing vesicles of ionic amphiphiles. Vesicles are ...

In the first part of this work we will study the spatial decay of solutions of nonlinear dispersive equations. The starting point will be the Korteweg-de Vries (KdV) equation, for which it will be proved that a decay of ...