Measure of noncompactness, surjectivity of gradient operators and an application to the p-Laplacian

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:471

Article

Chiappinelli, R.¹  Edmunds, D. E.² 

[1] Univ Siena, Dipartimento Ingn Informaz & Sci Matemat, I-53100 Siena, Italy

[2] Univ Sussex, Div Math, Brighton BN1 9QH, E Sussex, England

关键词: alpha-Coercivity;    Ekeland's variational principle;    Strongly monotone operator;    p-Laplacian;   

DOI  :  10.1016/j.jmaa.2018.11.010

来源: Elsevier

【 摘 要 】

It is shown that if X is a real Banach space with dual X* and F : X -> X* is a continuous gradient operator that is coercive in a certain sense and proper on closed bounded sets, then it is surjective. Use of the notion of measure of noncompactness enables sufficient conditions for properness to be given. These give rise to a surjectivity theorem for compact perturbations of strongly monotone maps and also facilitate discussion of a Dirichlet boundary-value problem involving the p-Laplacian. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free