arXiv subjects
Publications and source records attributed to Alessio Pomponio.
We consider a system of nonlinear Schrodinger equations with three waves interaction studying the existence of ground state solutions. In particular, we find a vector ground state, namely a ground state with the three components all different from zero.
In this paper we prove the existence of a nontrivial solution to the nonlinear Schrodinger-Maxwell equations in $\R^3,$ assuming on the nonlinearity the general hypotheses introduced by Berestycki & Lions.
In this paper we prove the existence of a ground state solution for the nonlinear Klein-Gordon-Maxwell equations in the electrostatic case.
In this paper we prove the existence of a positive solution to the equation $-Δu + V(x)u=g(u)$ 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.
We prove the existence of ground state solutions for the nonlinear Schrodinger-Maxwell equations with a singular potential.
We look for positive solutions to the nonlinear Schrodinger equation with a potential, under the hypothesis of zero mass on the nonlinearity, in a particular situation. Existence and multiplicity results are provided.
We prove the existence of ground state solutions for the nonlinear Schrodinger-Maxwell equations.
In this paper we present some compactness results, showing how they can be applied in dealing with "zero mass" problems by a variational approach. In particular we use our results in two different situations: we look for complex valued solutions of a very classical elliptic equation, and we study an elliptic problem on an axially symmetric unbounded domain.
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 $Σ$ 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 $Σ$ in the sense of subdifferential calculus.
Coupled nonlinear Schrodinger systems describe some physical phenomena such as the propagation in birefringent optical fibers, Kerr-like photorefractive media in optics and Bose-Einstein condensates. In this paper, we study the existence of concentrating solutions of a singularly perturbed coupled nonlinear Schrodinger system, in presence of potentials. We show how the location of the concentration points depends strictly on the potentials.
In this paper we study the existence of solutions and their concentration phenomena of a singularly perturbed semilinear Schrodinger equation with the presence of the critical Sobolev exponent.
In this paper we prove that a singularly perturbed Neumann problem with potentials admits the existence of interior spikes concentrating in maxima and minima of an auxiliary function depending only on the potentials.
We study the existence of concentrating solutions of a singularly perturbed Neumann problems with two potentials.
We prove the existence of one or more solutions to a singularly perturbed elliptic problema with two potential functions.
In this paper we obtain, for a semilinear elliptic problem in R^N, families of solutions bifurcating from the bottom of the spectrum of $-Δ$. The problem is variational in nature and we apply a nonlinear reduction method which allows us to search for solutions as critical points of suitable functionals defined on finite-dimensional manifolds.