5 papers
Optimizers for the finite-rank fractional Lieb--Thirring inequality
Lu Chen, Lianfeng Yang
The finite-rank fractional Lieb--Thirring inequality provides an estimate on the Riesz sum of the first negative eigenvalues of the fractional Schrödinger operator i…
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…