Luca Battaglia

activity

20132026

most citedExistence of groundstates for a class of nonlinear Choquard equations in the plane

38 citations · 135 across the 21 of their papers we have counts for

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Showing 2017Show all

3 papers · 1 filter

math.AP2017★ 22 cited

Groundstates of the Choquard equations with a sign-changing self-interaction potential

Luca Battaglia, Jean Van Schaftingen

We consider a nonlinear Choquard equation $- Δ u + u = (V * ∣ u ∣^{p}) ∣ u ∣^{p - 2} u in R^{N},$ when the self-interaction potential $V$ is unbounded from below. Under…

math.AP2017

Nonradial entire solutions for Liouville systems

Luca Battaglia, Francesca Gladiali, Massimo Grossi

We consider the following system of Liouville equations: $$\left\{\begin{array}{ll}-Δu_1=2e^{u_1}+μe^{u_2}&\text{in }\mathbb R^2\\-Δu_2=μe^{u_1}+2e^{u_2}&\text{in }\mathbb R^2\\\in…

math.AP2017

Ground state solutions for a nonlinear Choquard equation

Luca Battaglia

We discuss the existence of ground state solutions for the Choquard equation $- Δ u = (I_{α} * F (u)) F^{'} (u) in R^{N} .$ We prove the existence of solutions under…