英和和英

形容詞

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.
   • 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 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle f(0)\ <\ 0}"> f ( 0 )   <   0 {\displaystyle \scriptstyle f(0)\ <\ 0} <img loading="lazy" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b64d6db7c00c66c48da04e973281e19049955959" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.267ex; height:2.176ex;" alt="{\displaystyle \scriptstyle f(0)\ <\ 0}">,...then the eigenvalue problem is called semipositone...

派生語

• semipositone