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Existence, Uniqueness, Stability and Calculation of the Stationary Regimes in Some Nonlinear Systems

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Quantum Mechanics in Mathematics, Chemistry, and Physics

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Abstract

Consider a passive one-loop system consisting of a linear two-port L, a nonlinear two-port N and an electromotive force e(t) which are sequentially joined. Let i be the current in the system, then uL = Zi is the voltage on L, i = F(u) where u = uN is the voltage on N, Z is a linear operator, F is a nonlinear operator. The governing equation is

$$ u + ZFu = e $$
((1))

or

$$ Au + Fu = J,A = {Z^{{ - 1}}},J = Ae. $$
((2))

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    A. G. Ramm

Authors
  1. A. G. Ramm
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Editor information

Editors and Affiliations

  1. University of Colorado, Boulder, Colorado, USA

    Karl E. Gustafson  & William P. Reinhardt  & 

  2. Joint Institute for Laboratory Astrophysics, National Bureau Standards and University of Colorado, Boulder, Colorado, USA

    William P. Reinhardt

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© 1981 Plenum Press, New York

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Ramm, A.G. (1981). Existence, Uniqueness, Stability and Calculation of the Stationary Regimes in Some Nonlinear Systems. In: Gustafson, K.E., Reinhardt, W.P. (eds) Quantum Mechanics in Mathematics, Chemistry, and Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3258-9_24

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  • DOI: https://doi.org/10.1007/978-1-4613-3258-9_24

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3260-2

  • Online ISBN: 978-1-4613-3258-9

  • eBook Packages: Springer Book Archive

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