Generalized Schrodinger-Poisson type systems
In this paper we study some Schrodinger-Poisson type systems on a bounded domain, with Dirichlet boundary condition on both the variables.
math.AP↗
arXiv subjects
Pietro d'Avenia
Publications and source records attributed to Pietro d'Avenia.
On a system involving a critically growing nonlinearity
This paper deals with the system \[\{{array}{ll} -Δu = λu + q |u|^3 u ϕ& \hbox{in} B_R, -Δϕ=q |u|^5 & \hbox{in} B_R, u=ϕ=0 & \hbox{on} \partial B_R. {array}.\] We prove existence and nonexistence results depending on the value of $λ$.
math.AP↗
Infinitely many positive solutions for a Schrodinger-Poisson system
We find infinitely many positive non-radial solutions for a nonlinear Schrodinger-Poisson system.
math.AP↗
Multiple critical points for a class of nonlinear functionals
In this paper we prove a multiplicity result concerning the critical points of a class of functionals involving local and nonlocal nonlinearities. We apply our result to the nonlinear Schrodinger-Maxwell system and to the nonlinear elliptic Kirchhoff equation assuming on the local nonlinearity the general hypotheses introduced by Berestycki and Lions.
math.AP↗
On the Schrodinger-Maxwell equations under the effect of a general nonlinear term
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.
math.AP↗
Dirichlet and Neumann problems for Klein-Gordon-Maxwell systems
This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet boundary conditions on the matter field, and either Dirichlet or Neumann boundary conditions on the electric potential.
math.AP↗
Klein-Gordon-Maxwell System in a bounded domain
This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves $ψ=u(x)e^{-iωt}$ in equilibrium with a purely electrostatic field $\mathbf{E}=-\nablaϕ(x)$. We assume an homogeneous Dirichlet boundary condition on $u$ and an inhomogeneous Neumann boundary condition on $ϕ$. In the "linear" case we characterize the existence of nontrivial solutions for small boundary data. With a suitable nonlinear perturbation in the matter equation, we get the existence of infinitely many solutions.
math.AP↗