Nonexistence of Solutions to Kpp-type Equations of Dimension Greater than or Equal to One

@inproceedings{Simon2006NonexistenceOS,
  title={Nonexistence of Solutions to Kpp-type Equations of Dimension Greater than or Equal to One},
  author={P{\'e}ter L. Simon},
  year={2006}
}
In this article, we consider a semilinear elliptic equations of the form ∆u + f(u) = 0, where f is a concave function. We prove for arbitrary dimensions that there is no solution bounded in (0, 1). The significance of this result in probability theory is also discussed.