We consider the existence of weak solutions for 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. We also perform numerical simulations for specific examples usinf finite difference method.
Maximal and minimal weak solutions for elliptic coupled systems with nonlinearity on the boundary
Shalmali Bandyopadhyay, University of Tennessee MartinAuthors: Nsoki Mavinga, Thomas Lewis
2023 AWM Research Symposium
Advances in Partial Differential Equations and Applications [Organized by Maya Chhetri, Nsoki Mavinga and Irina Mitrea]