Zeng Liu, Vitaly Moroz
Published 2022-01-03Version 1
We study the Schr\"{o}dinger-Poisson-Slater equation $$-\Delta u + u+\lambda(I_{2}*|u|^2)u=|u|^{p-2}u\quad\text{in $\mathbb R^3$},$$ where $p\in (3,6)$ and $\lambda>0$. By using direct variational analysis based on the comparison of the ground state energy levels, we obtain a characterization of the limit profile of the positive ground states for $\lambda\to \infty$.
Asymptotic profiles for the Cauchy problem of damped beam equation with two variable coefficients and derivative nonlinearity
Positive ground states for a system of Schrödinger equations with critically growing nonlinearities
Uniqueness and Nondegeneracy of positive ground states of $ -Δu + (-Δ)^s u+u = u^{p+1} \quad \hbox{in $\mathbb{R}^n$}$
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