semipositone

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.
   • Leszek Gasinski, Nikolaos S. Papageorgiou (2004) Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems, CRC Press, →ISBN, page 704

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

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

     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 $\scriptstyle f(0)\ <\ 0$,...then the eigenvalue problem is called semipositone...