Maximal and minimal weak solutions for elliptic problems with nonlinearity on the boundary-Reference-Cited by-同舟云学术

Maximal and minimal weak solutions for elliptic problems with nonlinearity on the boundary

Published:2022 Issue:6 Volume:30 Page:2121-2137
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Bandyopadhyay S.¹,Chhetri M.¹,Delgado B. B.²,Mavinga N.³,Pardo R.⁴

Affiliation:

1. UNC Greensboro, Greensboro, NC 27402, USA

2. Universidad Autónoma de Aguascalientes, 20131 Aguascalientes, Mexico

3. Swarthmore College, Swarthmore, PA 19081, USA

4. Universidad Complutense de Madrid, 28040 Madrid, Spain

Abstract

<abstract><p>This paper deals with the existence of weak solutions for semilinear elliptic equation with nonlinearity on the boundary. We establish the existence of a maximal and a minimal weak solution between an ordered pair of sub- and supersolution for both monotone and nonmonotone nonlinearities. We use iteration argument when the nonlinearity is monotone. For the nonmonotone case, we utilize the surjectivity of a pseudomonotone and coercive operator, Zorn's lemma and a version of Kato's inequality.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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