Existence of Quasi-Solutions of Systems of Nonlinear Elliptic BVP’s Suggested by Biochemical Reactions

In all biochemical processes of practical interest such as fermentation of industries, pharmaceuticals and waste treatment, the reaction rates are influenced by diffusion and the equations are nonlinear [11,12], Several interacting populations related to ecology [10] as well as problems of chemical engineering [14] also yield nonlinear elliptic equations as a by-product. Since constructive proofs of existence, which can also provide numerical procedures for the computation of solutions, are of greater value than nonconstructive proofs, the method of upper and lower solutions coupled with the monotone iterative method has been, in recent years, employed to prove existence of multiple solutions of a variety of nonlinear problems [8].