Positive solution for semilinear elliptic equation on general domain Original Research Article

We give the comparison principle, the uniqueness theorem, and the necessary and sufficient conditions for the solvability with positive solutions in Wloc2,p∩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 refined a priori estimates and the degree theory.