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

Shalmali Bandyopadhyay | Zendy; Maya Chhetri | Zendy; Briceyda B. Delgado | Zendy; Nsoki Mavinga | Zendy; Rosa Pardo | Zendy

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Maximal 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.

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