We prove the uniqueness of the supersymmetric Salam-Sezgin (Minkowski) 4 ×S 2 ground state among all nonsingular solutions with a four-dimensional Poincaré, de Sitter or anti-de Sitter symmetry. We construct the most general solutions with an axial symmetry in the two-dimensional internal space, and show that included amongst these is a family that is non-singular away from a conical defect at ...

Ground-state properties of spherical even-even nuclei 14 ≤ Z ≤ 28 and N = 18, 20, 22 are described in the framework of Relativistic Hartree Bogoliubov (RHB) theory. The model uses the NL3 effective interaction in the mean-field Lagrangian, and describes pairing correlations by the pairing part of the finite range Gogny interaction D1S. Binding energies, two-proton separation energies, and proto...

We study the stability of traveling wave solutions to a fifth-order water wave model. By solving a constrained minimization problem we show that “ground state” traveling wave solutions exist. Their stability is shown to be determined by the convexity or concavity of a function d(c) of the wave speed c. The analysis makes frequent use of the variational properties of the traveling waves.

We establish global well-posedness and scattering for solutions to the masscritical nonlinear Hartree equation iut +∆u = ±(|x|−2 ∗ |u|2)u for large spherically symmetric L2x(R ) initial data; in the focusing case we require, of course, that the mass is strictly less than that of the ground state.

These are lecture notes from a course given at the summer school on ‘Current topics in Mathematical Physics’, held at Luminy in September 2013. We discuss ground state solutions for semi-linear PDEs in R . In particular, we prove their existence, radial symmetry and uniqueness up to translations.

In this paper, we consider the existence and concentration behavior of positive ground state solution to the following problem { −hΔpu+V (x)|u|p−2u = K(x)|u|q−2u+ |u|p−2u, x ∈ RN , u ∈W 1,p(RN ), u > 0, x ∈ RN , where h is a small positive parameter, 1 < p < N , max{p, p∗ − p p−1} < q < p∗ , p∗ = Np N−p is the critical Sobolev exponent, V (x) and K(x) are positive smooth functions. Under some n...

A class of 4-dimensional supersymmetric dyonic black hole solutions that arise in an effective 11-dimensional supergravity compactified on a 7-torus is presented. We give the explicit form of dyonic solutions with diagonal internal metric, associated with the Kaluza-Klein sector as well as the threeform field, and relate them to a class of solutions with a general internal metric by imposing a ...

We consider nonlinear Schrödinger equations iut +∆u+ β(|u| )u = 0 , for (t, x) ∈ R × R, where d ≥ 3 and β is smooth. We prove that symmetric finite energy solutions close to orbitally stable ground states converge to a sum of a ground state and a dispersive wave as t → ∞ assuming the so called Fermi Golden Rule (FGR) hypothesis. We improve the “sign condition”required in a recent paper by Gang ...

We study the instability of standing-wave solutions eφω(x) to the inhomogeneous nonlinear Schrödinger equation iφt = −4φ + |x|2φ− |x|b|φ|p−1φ, x ∈ R , where b > 0 and φω is a ground-state solution. The results of the instability of standing-wave solutions reveal a balance between the frequency ω of wave and the power of nonlinearity p for any fixed b > 0.

We analyze the behavior of positive solutions of elliptic equations with a degenerate logistic nonlinearity and Dirichlet boundary conditions. Our results concern existence and strong localization in the spatial region in which the logistic nonlinearity cancels. This type of nonlinearity has applications in the nonlinear Schrodinger equation and the study of Bose-Einstein condensates. In this c...