Uniform continuity and Brézis–Lieb-type splitting for superposition operators in Sobolev space-Reference-Cited by-同舟云学术

Uniform continuity and Brézis–Lieb-type splitting for superposition operators in Sobolev space

Published:2018-11-01 Issue:4 Volume:7 Page:587-599
ISSN:2191-9496
Container-title:Advances in Nonlinear Analysis
language:
Short-container-title:

Author:

Ackermann Nils¹

Affiliation:

1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510México D.F., Mexico

Abstract

AbstractUsing concentration-compactness arguments, we prove a variant of the Brézis–Lieb-Lemma under weaker assumptions on the nonlinearity than known before. An intermediate result on the uniform continuity of superposition operators in Sobolev space is of independent interest.

Funder

Consejo Nacional de Ciencia y Tecnología

Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/downloadpdf/journals/anona/7/4/article-p587.xml

Reference38 articles.

1. Bound states for semilinear Schrödinger equations with sign-changing potential;Calc. Var. Partial Differential Equations,2007

2. A relation between pointwise convergence of functions and convergence of functionals;Proc. Amer. Math. Soc.,1983

3. Infinite-dimensional homology and multibump solutions;J. Fixed Point Theory Appl.,2009

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