Positive Solution to a Nonlinear Elliptic Problem
Zeineb Ghardallou · Potential Analysis · 2016
Let L be a second order elliptic operator with smooth coefficients satisfying L1 = 0 defined in a domain Ω that is Greenian for L. Under fairly general hypotheses on the function φ, we solve the following problem: $$\left\{ \begin{array}{ll} Lu+\varphi(\cdot,u)=0, & \text{in the sense of distributions in \({\Omega}\);} \\ u>0, & \text{in \({\Omega}\) ;} \\ u=0, & \text{on \(\partial {\Omega}\).} \end{array} \right. $$