Open AccessMaximal and minimal weak solutions for elliptic problems with nonlinearity on the boundary
Author(s) -
Shalmali Bandyopadhyay,
Maya Chhetri,
Briceyda B. Delgado,
Nsoki Mavinga,
Rosa Pardo
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022107
Subject(s) - monotone polygon , mathematics , lemma (botany) , nonlinear system , pure mathematics , boundary (topology) , weak solution , operator (biology) , boundary value problem , mathematical analysis , physics , geometry , ecology , biochemistry , chemistry , poaceae , repressor , quantum mechanics , gene , transcription factor , biology
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.