semipositoneとは 意味・読み方・使い方

形容詞

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

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

     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...