semipositone

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

-𝛥x(z)=𝜆f(x(z)) fora.a.z∈𝛺,\x|_(∂𝛺),x>0

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