Research
Multiple blowing-up and concentrating solutions for Liouville-type equations with singular sources under mixed boundary conditions
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
Boundary Value Problems 2012, 2012:33 doi:10.1186/1687-2770-2012-33
Published: 23 March 2012Abstract
In this article, we mainly construct multiple blowing-up and concentrating solutions for a class of Liouville-type equations under mixed boundary conditions:
for ε small, where 
, Ω is a bounded, smooth domain in 
, Γ := {p1, ..., pN} ⊂ Ω is the set of singular sources, δp denotes the Dirac mass at p, ν denotes unit outward normal vector to ∂Ω and b(x) > 0 is a smooth function on ∂Ω.
2000 Mathematics Subject Classification: 35B25; 35J25; 35B38.
