@article{Bandyopadhyay2022, 
author = {S. Bandyopadhyay and M. Chhetri and B. B. Delgado and N. Mavinga and R. Pardo},
title = {Maximal and minimal weak solutions for elliptic problems with nonlinearity on the boundary},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {6},
pages = {2121-2137},
keywords = {elliptic problem, nonlinear boundary conditions, maximal and minimal weak solution, pseudomonotone operator, Kato's inequality},
url = {https://www.sciopen.com/article/10.3934/era.2022107},
doi = {10.3934/era.2022107},
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.}
}