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2 results

  • 13 - Uniqueness

  • from PART I - EQUILIBRIUM IN NATURAL WATERS
  • Craig M. Bethke, University of Illinois, Urbana-Champaign
  • Book:
    Geochemical and Biogeochemical Reaction Modeling
    Published online:
    09 December 2021
    Print publication:
    06 January 2022, pp 167-174

  • Summary

    Valid solutions to the multicomponent equilibrium problem are commonly but not invariably unique roots of the governing equations. Modelers for this reason need to consider the possibility of the existence of more than one mathematically correct root to the equations describing chemical equilibrium in multicomponent systems. This chapter demonstrates the origin of nonunique roots to the equilibrium problem, provides several worked examples of how such roots may arise, and gives advice about coping with the possibility of nonuniqueness.

  • Nonlinear Multipoint Boundary Value Problems for Second Order Differential Equations

  • Tadeusz Jankowski
  • Journal:
    Canadian Mathematical Bulletin / Volume 53 / Issue 3 / 01 September 2010
    Published online by Cambridge University Press:
    20 November 2018, pp. 475-490
    Print publication:
    01 September 2010
    • Article
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  • In this paper we shall discuss nonlinear multipoint boundary value problems for second order differential equations when deviating arguments depend on the unknown solution. Sufficient conditions under which such problems have extremal and quasi-solutions are given. The problem of when a unique solution exists is also investigated. To obtain existence results, a monotone iterative technique is used. Two examples are added to verify theoretical results.