INVESTIGADORES
DE LEO Mariano Fernando
artículos
Título:
On the existence of Ground States for Nonlinear Schrödinger-Poisson Equation
Autor/es:
DE LEO, MARIANO
Revista:
JOURNAL OF NONLINEAR ANALYSIS
Editorial:
PERGAMON-ELSEVIER SCIENCE LTD
Referencias:
Lugar: Amsterdam; Año: 2010 vol. 73 p. 979 - 986
ISSN:
0362-546X
Resumen:
This paper is concerned with the existence of ground states for the SchrödingerPoissonequation i u_t=-u_xx+V(u) u-f(|u|^2) u; where V(u) is a Hartree type nonlinearity,stemming from the coupling with the Poisson equation, which includes the so-calleddoping profile or impurities. By means of variational methods in the energy space we showthat ground states exist and belong to the Schwartz space of rapidly decreasing functionswhenever total charge not exceed some critical value, it is also shown that for values of thetotal charge greater than this critical value, energy is not bounded from below. In addition,we show that this critical value is the total charge given by the impurities
