Singularly perturbed Neumann problems with potentials

We study the existence of concentrating solutions of a singularly perturbed Neumann problems with two potentials.Comment: 24 pages, 1 figur

Oscillating solutions for prescribed mean curvature equations: Euclidean and Lorentz-Minkowski cases

This paper deals with the prescribed mean curvature equations both in the Euclidean case and in the Lorentz-Minkowski case in presence of a nonlinearity $g$ such that $g'(0)>0$. We show the existence of oscillating solutions, namely with an unbounded sequence of zeros. We show the existence of oscillating solutions, namely with an unbounded sequence of zeros. Moreover these solutions are periodic, if $N=1$, while they are radial symmetric and decay to zero at infinity with their derivatives, if $N\ge 2$.Comment: 11 page

On the Schrodinger equation in RNR^N under the effect of a general nonlinear term

In this paper we prove the existence of a positive solution to the equation $-\Delta u + V(x)u=g(u)$ in $R^N,$ assuming the general hypotheses on the nonlinearity introduced by Berestycki & Lions. Moreover we show that a minimizing problem, related to the existence of a ground state, has no solution.Comment: 18 page

Locating the peaks of semilinear elliptic systems

We consider a system of weakly coupled singularly perturbed semilinear elliptic equations. First, we obtain a Lipschitz regularity result for the associated ground energy function $\Sigma$ as well as representation formulas for the left and the right derivatives. Then, we show that the concentration points of the solutions locate close to the critical points of $\Sigma$ in the sense of subdifferential calculus.Comment: To appear on Advanced Nonlinear Studies, 21 page

Quasi-particle spectrum and entanglement generation after a quench in the quantum Potts spin chain

Recently, a non-trivial relation between the quasi-particle spectrum and entanglement entropy production was discovered in non-integrable quenches in the paramagnetic Ising quantum spin chain. Here we study the dynamics of analogous quenches in the quantum Potts spin chain. Tuning the parameters of the system, we observe a sudden increase in the entanglement production rate, which is shown to be related to the appearance of new quasiparticle excitations in the post-quench spectrum. Our results demonstrate the generality of the effect and support its interpretation as the non-equilibrium version of the well-known Gibbs paradox related to mixing entropy which appears in systems with a non-trivial quasi-particle spectrum.Comment: 15 pages, pdflatex, 30 pdf figures. v2: reformatted, 22 pages, typos correcte

Quasilinear elliptic equations in \RN via variational methods and Orlicz-Sobolev embeddings

In this paper we prove the existence of a nontrivial non-negative radial solution for a quasilinear elliptic problem. Our aim is to approach the problem variationally by using the tools of critical points theory in an Orlicz-Sobolev space. A multiplicity result is also given.Comment: 18 pages, 1 figur