View source for Positone

==English==

===Etymology===
{{blend|en|positive|monotone}}

===Adjective===
{{en-adj|-}}

# {{lb|en|mathematics}} of a particular kind of [[eigenvalue]] problem involving a [[nonlinear]] function on the [[real number|reals]] that is [[continuous]], positive, and [[monotone]].
#* {{cite-book|en|year=2004|author=Leszek Gasinski|author2=Nikolaos S. Papageorgiou|title=Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems|pageurl=http://books.google.co.uk/books?id=a1YVha-S6y4C&pg=PA704#v=onepage&q&f=true|page=704|publisher=CRC Press|isbn=1420035037}}
#*: Finally, we mention that several papers studied nonlinear eigenvalue problems of the form
#*:: <math>
\begin{cases}
-\Delta x(z) = \lambda f (x (z)) \text { for a.a. }z \in \Omega, \\
x|_{\partial \Omega},\ x \ge 0
\end{cases}
</math>
#*: for <math>\scriptstyle \lambda\ >\ 0 </math> under the assumption that <math>\scriptstyle f:\ \mathbb R\ \to\ \mathbb R</math> is continuous, positive, monotone. For this reason such problems were named '''''positone'''''... If the nonlinearity <math>\scriptstyle f:\ \mathbb R\ \to\ \mathbb R</math> is continuous, monotone and <math>\scriptstyle f(0)\ <\ 0 </math>,...then the eigenvalue problem is called ''semipositone''...

====Derived terms====
* {{l|en|semipositone}}
{{cln|en|terms prefixed with posi-}}

==Italian==

===Noun===
{{it-noun|m}}

# {{alternative form of|it|positrone}}

===Anagrams===
* {{anagrams|it|a=einoopst|pentosio|spoetino}}