Advertisement

Mathematical systems theory

, Volume 18, Issue 1, pp 251–256 | Cite as

A local implicit function theorem and application to systems of differential equations

  • Vaclav Dolezal
  • Shiva Shankar
Article

Abstract

A local implicit function theorem is proved which assumes certain injectivity rather than differentiability. Moreover, there is given a result on solvability of noncanonic systems of differential equations which arise in optimal control and network theory.

Keywords

Differential Equation Computational Mathematic Network Theory Implicit Function Theorem Local Implicit Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. T. Schwartz,Nonlinear Functional Analysis, Gordon and Breach Science Publ., 1969, 77.Google Scholar
  2. 2.
    I. W. Sandberg, Global implicit function theorems,IEEE Trans. Circ. and Syst., Vol. CAS-28, 145–149 (1981).Google Scholar
  3. 3.
    M. Spivak,Differential Geometry, Vol. I, Publish or Perish, Inc. 1979, p. 56.Google Scholar
  4. 4.
    J. Dieudonné,Foundations of Modern Analysis, Academic Press, 1960, p. 268Google Scholar
  5. 5.
    J. K. Hale,Ordinary Differential Equations, Wiley-Interscience, 1969, p. 14.Google Scholar
  6. 6.
    S. L. Campbell and C. D. Meyer, Jr.,Generalized Inverses of Linear Transformations, Pitman Publ. Co., 1979.Google Scholar
  7. 7.
    R. W. Newcomb, The semistate description of nonlinear time-variable circuits,IEEE Trans. CAS, Vol. CAS-28 62–71 (1981).Google Scholar

Copyright information

© Springer-Verlag New York Inc 1985

Authors and Affiliations

  • Vaclav Dolezal
    • 1
  • Shiva Shankar
    • 2
  1. 1.Department of Applied Mathematics and StatisticsState University of New York at Stony BrookStony BrookUSA
  2. 2.TATA Institute of Fundamental ResearchIndian Institute of ScienceBangaloreIndia

Personalised recommendations