Semilinear elliptic boundary-value problems on bounded multiconnected domains

Abstract

A semilinear elliptic boundary-value problem on bounded multiconnected domains is studied. The authors prove that under suitable conditions, the problem may have no solutions in certain cases and many have one or two nonnegative solutions in some other cases. The radial solutions were also studied in annular domains.

Keywords

• Semilnear elliptic boundary-value problem
• nonnegative solution
• radial solution
• nonexistence
• existence
• multiplicity.