different between semipositone vs positone

English

Etymology

semi- +? positone

Adjective

semipositone (not comparable)

1. (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, page 704

     Finally, we mention that several papers studied nonlinear eigenvalue problems of the form

     ${\displaystyle {\begin{cases}-\Delta x(z)=\lambda f(x(z)){\text{ for a.a. }}z\in \Omega ,\\x|_{\partial \Omega },\ x\geq 0\end{cases}}}$

     for ${\displaystyle \scriptstyle \lambda \ >\ 0}$ under the assumption that ${\displaystyle \scriptstyle f:\ \mathbb {R} \ \to \ \mathbb {R} }$ is continuous, positive, monotone. For this reason such problems were named positone... If the nonlinearity ${\displaystyle \scriptstyle f:\ \mathbb {R} \ \to \ \mathbb {R} }$ is continuous, monotone and ${\displaystyle \scriptstyle f(0)\ <\ 0}$,...then the eigenvalue problem is called semipositone...

English

Etymology

Blend of positive +? monotone

Adjective

positone (not comparable)

1. (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, page 704

     Finally, we mention that several papers studied nonlinear eigenvalue problems of the form

     ${\displaystyle {\begin{cases}-\Delta x(z)=\lambda f(x(z)){\text{ for a.a. }}z\in \Omega ,\\x|_{\partial \Omega },\ x\geq 0\end{cases}}}$

     for ${\displaystyle \scriptstyle \lambda \ >\ 0}$ under the assumption that ${\displaystyle \scriptstyle f:\ \mathbb {R} \ \to \ \mathbb {R} }$ is continuous, positive, monotone. For this reason such problems were named positone... If the nonlinearity ${\displaystyle \scriptstyle f:\ \mathbb {R} \ \to \ \mathbb {R} }$ is continuous, monotone and ${\displaystyle \scriptstyle f(0)\ <\ 0}$,...then the eigenvalue problem is called semipositone...

Derived terms

• semipositone

Italian

Noun

positone m (plural positoni)

1. Alternative form of positrone