A multiplicity result for double singularly perturbed elliptic systems

We show that the number of low energy solutions of a double singularly perturbed Schroedinger Maxwell system type on a smooth 3 dimensional manifold (M,g) depends on the topological properties of the manifold. The result is obtained via Lusternik Schnirelmann category theory

The Emergence of Law Consultants

In this paper we study a slightly subcritical Choquard problem on a bounded domain A. We prove that the number of positive solutions depends on the topology of the domain. In particular when the exponent of the nonlinearity approaches the critical one, we show the existence of cat (A) + 1 solutions. Here cat (A) denotes the Lusternik–Schnirelmann category

Nonlinear Klein-Gordon-Maxwell systems with Neumann boundary conditions on a Riemannian manifold with boundary

Let (M,g) be a smooth compact, n dimensional Riemannian manifold, n=3,4 with smooth n-1 dimensional boundary. We search the positive solutions of the singularly perturbed Klein Gordon Maxwell Proca system with homogeneous Neumann boundary conditions or for the singularly perturbed Klein Gordon Maxwell system with mixed Dirichlet Neumann homogeneous boundary conditions. We prove that stable critical points of the mean curvature of the boundary generates solutions when the perturbation parameter is sufficiently small.Comment: arXiv admin note: text overlap with arXiv:1410.884

Soliton dynamics of NLS with singular potentials

We investigate the validity of a soliton dynamics behavior in the semi-classical limit for the nonlinear Schroedinger equation in R^N,N≥3, in presence of a singular external potential

Peaked and low action solutions of NLS equations on graphs with terminal edges

We consider the nonlinear Schroedinger equation with focusing power-type nonlinearity on compact graphs with at least one terminal edge, i.e., an edge ending with a vertex of degree 1. On the one hand, we introduce the associated action functional, and we provide a profile description of positive low action solutions at large frequencies, showing that they concentrate on one terminal edge, where they coincide with suitable rescaling of the unique solution to the corresponding problem on the half-line. On the other hand, a Lyapunov-Schmidt reduction procedure is performed to construct one-peaked and multipeaked positive solutions with sufficiently large frequency, exploiting the presence of one or more terminal edges

Determination of carbonyl compounds in exhaled breath by on-sorbent derivatization coupled with thermal desorption and gas chromatography-tandem mass spectrometry

A reliable method for the determination of carbonyl compounds in exhaled breath based on on-sorbent derivatization coupled with thermal desorption and gas chromatography-tandem mass spectrometry is described. The analytical performances were optimized for a mixture of C2-C9 aldehydes and C3-C9 ketones, particularly interesting for clinical applications, by using an internal standard and applying a 2^3 full factorial design. A volume of sample (250 ml) was loaded at 50 ml min-1 into a Tenax GR sorbent tube containing 130 nmol of O-(2,3,4,5,6-pentafluorobenzyl)hydroxylamine hydrochloride. All compounds showed a limit of detection lower than 200 pptv. The yield of the derivatization procedure was normalized by adding to the sample a known amount of 6D-acetone as an internal standard. This allowed halving the relative standard deviation to 10% and 15% for the mono-and di-carbonyl compounds, respectively, thus improving reliability. The optimized method was applied to the determination of carbonyl compounds in 12 breath samples collected from four patients suffering from heart failure during hospitalization

Multi-solitary waves for the nonlinear Klein-Gordon equation

International audienceWe consider the nonlinear Klein-Gordon equation in $\R^d$. We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the composing boosted standing waves are stable. It is obtained by solving the equation backward in time around a sequence of approximate multi-solitary waves and showing convergence to a solution with the desired property. The main ingredients of the proof are finite speed of propagation, variational characterizations of the profiles, modulation theory and energy estimates

On the stability of standing waves of Klein-Gordon equations in a semiclassical regime

We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.Comment: 9 page