Esposito, Pierpaolo Blowup solutions for a Liouville equation with singular data. (English) Zbl 1162.35350 SIAM J. Math. Anal. 36, No. 4, 1310-1345 (2005). Summary: We study the existence of multiple blowup solutions for a semilinear elliptic equation with homogeneous Dirichlet boundary condition, exponential nonlinearity, and a singular source term given by Dirac masses. In particular, we extend the result of S. Baraket and F. Pacard [Calc. Var. Partial Differ. Equ. 6, No. 1, 1–38 (1998; Zbl 0890.35047)] by allowing the presence, in the equation, of a weight function possibly vanishing in some points. Cited in 38 Documents MSC: 35J20 Variational methods for second-order elliptic equations 35J25 Boundary value problems for second-order elliptic equations 35J60 Nonlinear elliptic equations Keywords:Liouville equation; singular data; exponential nonlinearity; blowup solutions Citations:Zbl 0890.35047 PDFBibTeX XMLCite \textit{P. Esposito}, SIAM J. Math. Anal. 36, No. 4, 1310--1345 (2005; Zbl 1162.35350) Full Text: DOI