25 citations · 49 across the 19 of their papers we have counts for
4 papers · 2 filters
On the embedding of weighted Sobolev spaces with applications to a planar nonlinear Schrödinger equation
Antonio Azzolini, Alessio Pomponio, Simone Secchi
In this paper we study the embedding properties for the weighted Sobolev space into the Lebesgue weighted space . Here and are di…
Nonlinear scalar field equation with point interaction
Alessio Pomponio, Tatsuya Watanabe
This paper is devoted to the study of the nonlinear scalar field equation with a point interaction at the origin in dimensions two and three. By applying the mountain pass theorem…
New insights into the solutions of a class of anisotropic nonlinear Schrödinger equations on the plane
Amin Esfahani, Hichem Hajaiej, Alessio Pomponio
In this paper, we study the following anisotropic nonlinear Schrödinger equation on the plane, \[ \begin{cases} {\rm i}\partial_t Φ+\partial_{xx} Φ-D_y^{2s} Φ+|Φ|^{p-2}Φ=0,&\quad (…
Schrödinger equation in dimension two with competing logarithmic self-interaction
Antonio Azzollini, Pietro d'Avenia, Alessio Pomponio
In this paper we study the equation \[ -Δu +(\log |\cdot|*|u|^2)u=(\log|\cdot|*|u|^q)|u|^{q-2}u, \qquad \hbox{ in }\mathbb{R}^2, \] where . By means of variational arg…