Semipositone

English

Etymology

From Template:Prefix.

Adjective

1. Template:Lb an eigenvalue problem that would be a positone eigenvalue problem except that the nonlinear function is not positive when its argument is zero.
   • Template:Cite-book

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

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

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