Positive solution for semilinear elliptic equation on general domain

✍ Scribed by Jiguang Bao

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 150 KB
• Volume: 53
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(03)00054-3

✦ Synopsis

We give the comparison principle, the uniqueness theorem, and the necessary and su cient conditions for the solvability with positive solutions in W 2;p loc ∩ L ∞ of the Dirichlet problems for semilinear elliptic equations on general bounded domains. The domains may be irregular while the equations are in general form. The resultant theorem includes previous work either in sublinear and some superlinear cases on the smooth domains or in linear case on the general domains. Our methods are the reÿned a priori estimates and the degree theory.