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

Carlo Mercuri, Vitaly Moroz Orcid Logo, Jean Van Schaftingen

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

Swansea University Authors: Carlo Mercuri, Vitaly Moroz Orcid Logo

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DOI (Published version): 10.1007/s00526-016-1079-3

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
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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: Faculty of Science and Engineering
Issue: 6

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