Special Session 75: Recent developments in Nonlinear PDEs, non-uniformly elliptic problems and related topics

Maximal and minimal weak solutions for elliptic coupled systems with nonlinearity on the boundary

Shalmali Bandyopadhyay
University of North Carolina at Greensboro
India
Co-Author(s):    Nsoki M Mavinga, Thomas Lewis
Abstract:
We consider the existence of weak solutions for semilinear elliptic coupled system with quasimonotone non decreasing 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.