Numerical verification method for positiveness of solutions to elliptic   equations
  In this paper, we propose a numerical method for verifying the positiveness of solutions to semilinear elliptic equations. We provide a sufficient condition for a solution to an elliptic equation to be positive in the domain of the equation, which can be checked numerically without requiring a complicated computation. We present some numerical examples. 
Kazuaki Tanaka, Kouta Sekine, and Shin'ichi Oishi
math.NA math.AP math.FA