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...