Potential Analysis

, Volume 44, Issue 3, pp 449–472 | Cite as

Positive Solution to a Nonlinear Elliptic Problem

  • Zeineb GhardallouEmail author
Open Access


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. $$


Nonlinear elliptic problems Regular domain Greenian domain Green function 

Mathematic Subject Classifications (2010)

31C05 31D05 35J60 


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Authors and Affiliations

  1. 1.Faculty of Sciences of Tunis, Department of Mathematical Analysis and ApplicationsUniversity Tunis El ManarTunisTunisia
  2. 2.Institute of MathematicsUniversity of WroclawWroclawPoland

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