Nonlinear vs Positone - What's the difference?

As adjectives the difference between nonlinear and positone

is that nonlinear is (of a set of points) not lying on a straight line while positone is (mathematics) of a particular kind of eigenvalue problem involving a nonlinear function on the reals that is continuous, positive, and monotone.

nonlinear

English

Alternative forms

* non-linear

Adjective

(-)

(of a set of points) not lying on a straight line

(chemistry, of a molecule) whose atoms do not lie in a straight line

(mathematics, of a function) having a product of independent variables, or a variable with an exponent not equal to one

(of a system) whose output is not directly proportional to its input

erratic and unpredictable; tending to jump back and forth

a film with a nonlinear plot

Antonyms

* linear

Derived terms

* nonlinearity

positone

English

Adjective

(en adjective)

(mathematics) of a particular kind of eigenvalue problem involving a nonlinear function on the reals that is continuous, positive, and monotone.

* 2004 , Leszek Gasinski, Nikolaos S. Papageorgiou, Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems , CRC Press, 2004 ISBN 1420035037, 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 \ge 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 $\scriptstyle f(0)\ <\ 0$ ,...the the eigenvalue problem is called ''semipositone ...

Derived terms

*semipositone