Schrödinger–Poisson system with singular potential

Schrödinger-Maxwell equations with a singular potential

In this paper we find a ground state solution for the nonlinear Schrödinger-Maxwell equations { −∆u+ V (x)u+ φu = |u|p−1u in R3, −∆φ = u2 in R3. where V is a possibly singular potential and 3 < p < 5.

Spectral Boundary-value Problems for the Dirac System with a Singular Potential

Robust H_∞ Controller design based on Generalized Dynamic Observer for Uncertain Singular system with Disturbance

This paper presents a robust ∞_H controller design, based on a generalized dynamic observer for uncertain singular systems in the presence of disturbance. The controller guarantees that the closed loop system be admissible. The main advantage of this method is that the uncertainty can be found in the system, the input and the output matrices. Also the generalized dynamic observer is used to est...

Initial value problems for diffusion equations with singular potential

Let V be a nonnegative locally bounded function defined inQ∞ := R × (0,∞). We study under what conditions on V and on a Radon measure μ in R does it exist a function which satisfies ∂tu−∆u+ V u = 0 in Q∞ and u(., 0) = μ. We prove the existence of a subcritical case in which any measure is admissible and a supercritical case where capacitary conditions are needed. We obtain a general representat...

On Hill's Equation with a Singular Complex-valued Potential

1. Introduction The differential equation y00 ‡ qy ˆ Ey is called Hill's equation if q is a realvalued, periodic, locally integrable function of a real variable. It is very well known that the spectrum of the operator associated with this equation consists of a countably in®nite number of compact intervals of the real line. These intervals are called (spectral) bands and are generally separated...