arXiv subjects
Publications and source records attributed to Antonio Azzollini.
In this paper we use a concentration and compactness argument to prove the existence of a nontrivial nonradial solution to the nonlinear Schrodinger-Poisson equations in R3, assuming on the nonlinearity the general hypotheses introduced by Berestycki & Lions
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 consider the nonlinear equation involving differential forms on a compact Riemannian manifold $δd ξ= f'(<ξ,ξ>)ξ$. This equation is a generalization of the semilinear Maxwell equations recently introduced in a paper by Benci and Fortunato. We obtain a multiplicity result both in the positive mass case (i.e. $f'(t)\geqε>0$ uniformly) and in the zero mass case ($f'(t)\geq 0$ and $f'(0)=0$) where a strong convexity hypothesis on the nonlinearity is assumed.
In this paper we look for solutions of a semilinear Maxwell type equation, in even dimension, greater than four. These solutions are critical points of a functional which is strongly degenerate because of the presence of the exterior derivative. We prove that, assuming a suitable convexity condition on the nonlinearity, the equation possesses infinitely many finite energy solutions.
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.