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math.AP2025
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,…
math.AP2025
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…
math.AP2025
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,\…