We consider 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. To prove the result, we utilize the surjectivity of a pseudomonotone and coercive operator, Zorn's lemma and a version of Kato's inequality.
Maximal and minimal weak solutions for elliptic problems with nonlinearity on the boundary
Shalmali Bandyopadhyay, University of North Carolina at GreensboroAuthors: Maya Chhetri, Briceyda Delgado, Nsoki Mavinga, Rosa Pardo
2022 AWM Research Symposium
Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows