In this paper we study the nonlinear Schrödinger-Maxwell equations { −∆u+ V (x)u+ φu = |u|p−1u in R3, −∆φ = u2 in R3. If V is a positive constant, we prove the existence of a ground state solution (u, φ) for 2 < p < 5. The non-constant potential case is treated under suitable geometrical assumptions on V , for 3 < p < 5. Existence and non-existence results are proved also when the nonlinearity ...

Abstract In this paper, we study the following generalized Kadomtsev-Petviashvili equation u t + x ( h ) = D − 1 <m:mi ma...

The time-dependent density-matrix theory (TDDM) gives a correlated ground state as a stationary solution of the time-dependent equations for one-body and two-body density matrices. The small amplitude limit of TDDM (STDDM) is a version of extended RPA theories which include the effects of ground state correlations. It is shown that the solutions of the Hartree-Fock Bogoliubov theory and the qua...

In this paper, we generalize the definitions of approximately inner $C_0$-groups and their ground states to the two- parameter case and study necessary and sufficient conditions for a state to be ground state. Also we prove that any approximately inner two- parameter $C_0$--group must have at least one ground state. Finally some applications are given.

A multi-channel algebraic scattering theory, to find solutions of coupled-channel scattering problems with interactions determined by collective models, has been structured to ensure that the Pauli principle is not violated. Positive (scattering) and negative (sub-threshold) solutions can be found to predict both the compound nucleus sub-threshold spectrum and all resonances due to coupled-chan...

We study the correlation energy associated with the pair fluctuations in BCS theory. We use a schematic two-level pairing model and discuss the behavior of the correlation energy across shell closures, including the even-odd differences. It is shown that the random phase approximation (RPA) to the ground state energy reproduces the exact solutions quite well both in the normal fluid and in the ...

We establish global existence, scattering for radial solutions to the energy-critical focusing Hartree equation with energy and Ḣ norm less than those of the ground state in R× R, d ≥ 5.

We consider the focusing mass-critical nonlinear Schrödinger equation and prove that blowup solutions to this equation with initial data in H(R), s > s0(d) and d ≥ 3, concentrate at least the mass of the ground state at the blowup time. This extends recent work by J. Colliander, S. Raynor, C. Sulem, and J. D. Wright, [13], T. Hmidi and S. Keraani, [21], and N. Tzirakis, [36], on the blowup of t...