Document Type
Article
Publication Date
2022
Published In
Electronic Research Archive
Abstract
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.
Keywords
elliptic problem, nonlinear boundary conditions, maximal and minimal weak solution, pseudomonotone operator, Kato's inequality
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
S. Bandyopadhyay, M. Chhetri, B. B. Delgado, Nsoki Mavinga, and R. Pardo.
(2022).
"Maximal And Minimal Weak Solutions For Elliptic Problems With Nonlinearity On The Boundary".
Electronic Research Archive.
Volume 30,
Issue 6.
2121-2137.
DOI: 10.3934/era.2022107
https://works.swarthmore.edu/fac-math-stat/290
Comments
This work is freely available under a Creative Commons license.