Shalmali Bandyopadhyay, University of Tennessee Martin
Authors: Nsoki Mavinga, Thomas Lewis
2023 AWM Research Symposium
Advances in Partial Differential Equations and Applications [Organized by Maya Chhetri, Nsoki Mavinga and Irina Mitrea]

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.

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