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arXiv · 1604.03294

Existence of groundstates for a class of nonlinear Choquard equations in the plane

Luca Battaglia·Jean Van Schaftingen
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Abstract

We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equation $$ -Δu+u=(I_α*F(u))F'(u)\qquad\text{in }\mathbb{R}^2, $$ where $I_α$ is the Riesz potential of order $α$ on the plane $\mathbb{R}^2$ under general nontriviality, growth and subcriticality on the nonlinearity $F \in C^1 (\mathbb{R},\mathbb{R})$.

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Luca Battaglia, Jean Van Schaftingen. 2017-01-11. Existence of groundstates for a class of nonlinear Choquard equations in the plane. https://doi.org/10.1515/ans-2016-0038

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