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Maximal And Minimal Weak Solutions For Elliptic Problems With Nonlinearity On The Boundary, S. Bandyopadhyay, M. Chhetri, B. B. Delgado, Nsoki Mavinga, R. Pardo

Mathematics & Statistics Faculty Works

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.