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Semipositone vs Positone - What's the difference?

semipositone | positone | Derived terms |

Semipositone is a derived term of positone.


In mathematics|lang=en terms the difference between semipositone and positone

is that semipositone is (mathematics) an eigenvalue problem that would be a positone eigenvalue problem except that the nonlinear function is not positive when its argument is zero while positone is (mathematics) of a particular kind of eigenvalue problem involving a nonlinear function on the reals that is continuous, positive, and monotone.

As adjectives the difference between semipositone and positone

is that semipositone is (mathematics) an eigenvalue problem that would be a positone eigenvalue problem except that the nonlinear function is not positive when its argument is zero while positone is (mathematics) of a particular kind of eigenvalue problem involving a nonlinear function on the reals that is continuous, positive, and monotone.

semipositone

English

Adjective

(en adjective)
  • (mathematics) an eigenvalue problem that would be a positone eigenvalue problem except that the nonlinear function is not positive when its argument is zero.
  • * 2004 , Leszek Gasinski, Nikolaos S. Papageorgiou, Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems , CRC Press, 2004 ISBN 1420035037, page 704
  • Finally, we mention that several papers studied nonlinear eigenvalue problems of the form
  • *::
  • \begin{cases} -\Delta x(z) = \lambda f (x (z)) \text { for a.a. }z \in \Omega, \\ x, _{\partial \Omega},\ x \ge 0 \end{cases}
  • *:for \scriptstyle \lambda\ >\ 0 under the assumption that \scriptstyle f:\ \mathbb R\ \to\ \mathbb R is continuous, positive, monotone. For this reason such problems were named positone'''''... If the nonlinearity \scriptstyle f:\ \mathbb R\ \to\ \mathbb R is continuous, monotone and \scriptstyle f(0)\ <\ 0 ,...the the eigenvalue problem is called '''''semipositone ...
  • positone

    English

    Adjective

    (en adjective)
  • (mathematics) of a particular kind of eigenvalue problem involving a nonlinear function on the reals that is continuous, positive, and monotone.
  • * 2004 , Leszek Gasinski, Nikolaos S. Papageorgiou, Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems , CRC Press, 2004 ISBN 1420035037, page 704
  • Finally, we mention that several papers studied nonlinear eigenvalue problems of the form
  • *::
  • \begin{cases} -\Delta x(z) = \lambda f (x (z)) \text { for a.a. }z \in \Omega, \\ x, _{\partial \Omega},\ x \ge 0 \end{cases}
  • *:for \scriptstyle \lambda\ >\ 0 under the assumption that \scriptstyle f:\ \mathbb R\ \to\ \mathbb R is continuous, positive, monotone. For this reason such problems were named positone'' ... If the nonlinearity \scriptstyle f:\ \mathbb R\ \to\ \mathbb R is continuous, monotone and \scriptstyle f(0)\ <\ 0 ,...the the eigenvalue problem is called ''semipositone ...
  • Derived terms

    *semipositone