890 citations · 3k across the 39 of their papers we have counts for
5 papers · 1 filter
Existence of groundstates for a class of nonlinear Choquard equations
Vitaly Moroz, Jean Van Schaftingen
We prove the existence of a nontrivial solution (u \in H^1 (\R^N)) to the nonlinear Choquard equation [- Δu + u = \bigl(I_α\ast F (u)\bigr) F' (u) \quad \text{in (\R^N),}] where (I…
Nonlocal Hardy type inequalities with optimal constants and remainder terms
Vitaly Moroz, Jean Van Schaftingen
Using a groundstate transformation, we give a new proof of the optimal Stein-Weiss inequality of Herbst [\int_{\R^N} \int_{\R^N} \frac{φ(x)}{\abs{x}^\fracα{2}} I_α(x - y) \frac{φ(y…
Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
Vitaly Moroz, Jean Van Schaftingen
We consider a semilinear elliptic problem [- Δu + u = (I_α\ast \abs{u}^p) \abs{u}^{p - 2} u \quad\text{in (\mathbb{R}^N),}] where (I_α) is a Riesz potential and (p>1). This family…
Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains
Vitaly Moroz, Jean Van Schaftingen
We consider a semilinear elliptic problem with a nonlinear term which is the product of a power and the Riesz potential of a power. This family of equations includes the Choquard o…
Asymptotic properties of ground states of scalar field equations with a vanishing parameter
Vitaly Moroz, Cyrill B. Muratov
We study the leading order behaviour of positive solutions of the equation -Δu +\varepsilon u-|u|^{p-2}u+|u|^{q-2}u=0,\qquad x\in\R^N, where , and when $\varepsilon…