POSITIVE SOLUTIONS WITH WEAK ISOLATED SINGULARITIES TO SOME SEMILINEAR ELLIPTIC EQUATIONS

Abstract

We are concerned with the existence of positive solutions with prescribed weak isolated singularities to some semilinear elliptic equations. The existence property differs with the behavior of the nonlinear term. Under the positivity assumption and a growth condition on the nonlinear term, we obtain not only solutions with a finite number of singularities but also those with infinitely many singularities. We show also that, for some nonlinear terms which changes sign, there is no solution with prescribed singular behavior.