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Potential Analysis

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

Positive Solution to a Nonlinear Elliptic Problem

  • Zeineb Ghardallou
Open Access
Article
  • 301 Downloads

Abstract

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. $$

Keywords

Nonlinear elliptic problems Regular domain Greenian domain Green function 

Mathematic Subject Classifications (2010)

31C05 31D05 35J60 

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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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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