463 citations · 937 across the 45 of their papers we have counts for
52 papers
Existence and Limiting Profiles of Normalized Travelling Wave Solutions for the Pseudo-Relativistic Schrödinger Equation with Logarithmic Nonlinearity
Pietro d'Avenia, Qihan He, Alessio Pomponio +1
We study the existence and asymptotic behaviour of normalized solutions to the following pseudo-relativistic Schrödinger equation with logarithmic nonlinearity \[ (\sqrt{-Δ+m^2 }-m…
Boosted Ground States for a Pseudo-Relativistic Schrödinger Equation with a double power nonlinearity
Pietro d'Avenia, Alessio Pomponio, Gaetano Siciliano +1
In this paper, we investigate the existence and limit behaviours of travelling solitary waves of the form to the nonlinear pseudo-relativistic Sc…
On a zero mass Schrödinger-Bopp-Podolsky system: ground states, nonexistence results and asymptotic behaviour
Alessio Pomponio, Lianfeng Yang
In this paper, we consider the following zero mass Schrödinger-Bopp-Podolsky system \[ \begin{cases} -Δu +q^2ϕu=|u|^{p-2}u, -Δϕ+a^2Δ^2ϕ=4πu^2, \end{cases} \text{ in } \mathbb{R}^3,…
On a nonlinear Schrödinger-Bopp-Podolsky system in the zero mass case: functional framework and existence
Erasmo Caponio, Pietro d'Avenia, Alessio Pomponio +2
In this paper, we consider in the following zero mass Schrödinger-Bopp-Podolsky system \[ \begin{cases} -Δu +q^2ϕu=|u|^{p-2}u\\ -Δϕ+a^2Δ^2ϕ=4πu^2 \end{cases} \] wher…
Coupled nonlinear Schrödinger equations with point interaction: existence and asymptotic behaviour
Yuki Osada, Alessio Pomponio
In this paper we deal with the following weakly coupled nonlinear Schrödinger system \begin{align*} \begin{cases} - Δ_αu + ωu = |u|^2 u + βu |v|^2&\quad \mathrm{in}\ \mathbb{R}^2,\…
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…