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Groundstates and radial solutions to nonlinear Schrödinger–Poisson–Slater equations at the critical frequency

Carlo Mercuri Orcid Logo, Vitaly Moroz Orcid Logo, Jean Van Schaftingen

Calculus of Variations and Partial Differential Equations, Volume: 55, Issue: 6

Swansea University Authors: Carlo Mercuri Orcid Logo, Vitaly Moroz Orcid Logo

Abstract

We introduce a functional space which is suitable for the variational analysis of a class of semilinear elliptic equations involving nonlocal potentials, we study the embeddings into L^p spaces given by a new class of Gagliardo-Nirenberg type inequalities, and we prove existence of solutions in both...

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Published in: Calculus of Variations and Partial Differential Equations
ISSN: 0944-2669 1432-0835
Published: 2016
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa30794
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Abstract: We introduce a functional space which is suitable for the variational analysis of a class of semilinear elliptic equations involving nonlocal potentials, we study the embeddings into L^p spaces given by a new class of Gagliardo-Nirenberg type inequalities, and we prove existence of solutions in both a radial and a nonradial setting.
Keywords: Gagliardo-Nirenberg inequalities, embeddings, RIesz kernel, Schödinger-Poisson systems.
College: College of Science
Issue: 6