On a result by Boccardo-Ferone-Fusco-Orsina

Via a symmetric version of Ekeland's principle recently obtained by the author we improve, in a ball or an annulus, a result of Boccardo-Ferone-Fusco-Orsina on the properties of minimizing sequences of functionals of calculus of variations in the non-convex setting.Comment: 5 page

On the symmetry of minimizers in constrained quasi-linear problems

We provide a simple proof of the radial symmetry of any nonnegative minimizer for a general class of quasi-linear minimization problems.Comment: 18 page

Soliton dynamics for the nonlinear Schr\"odinger equation with magnetic field

The semiclassical limit of a nonlinear focusing Schr\"odinger equation in presence of nonconstant electric and magnetic potentials V,A is studied by taking as initial datum the ground state solution of an associated autonomous elliptic equation. The concentration curve of the solutions is a parameterization of the solutions of a Newton ODE involving the electric force as well as the magnetic force via the Lorenz law of electrodynamics.Comment: 30 pages, 2 figure

Spike solutions for a class of singularly perturbed quasilinear elliptic equations

By means of a penalization scheme due to del Pino and Felmer, we prove the existence of single-peaked solutions for a class of singularly perturbed quasilinear elliptic equations associated with functionals which lack of smoothness. We don't require neither uniqueness assumptions on the limiting autonomous equation nor monotonicity conditions on the nonlinearity. Compared with the semilinear case some difficulties arise and the study of concentration of the solutions needs a somewhat involved analysis in which the Pucci-Serrin variational identity plays an important role.Comment: will appear in: Nonlinear Anal. TM

Symmetry of n-mode positive solutions for two-dimensional H\'enon type systems

We provide a symmetry result for n-mode positive solutions of a general class of semi-linear elliptic systems under cooperative conditions on the nonlinearities. Moreover, we apply the result to a class of H\'enon systems and provide the existence of multiple n-mode positive solutions.Comment: 8 page

Multiple solutions to logarithmic Schrodinger equations with periodic potential

We study a class of logarithmic Schrodinger equations with periodic potential which come from physically relevant situations and obtain the existence of infinitely many geometrically distinct solutions.Comment: 3 pages, corrigendum to version

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