Multiple blowing-up and concentrating solutions for Liouville-type equations with singular sources under mixed boundary conditions

作者：Chang, Yibin^*; Yang, Haitao

来源：Boundary Value Problems, 2012, 33.

DOI：10.1186/1687-2770-2012-33

• multiple blowing-up and concentrating solution
• Liouville-type equation
• singular source
• mixed boundary conditions
• finite dimensional reduction

In this article, we mainly construct multiple blowing-up and concentrating solutions for a class of Liouville-type equations under mixed boundary conditions:
{-Delta v = epsilon(2)e(v) - 4 pi Sigma(N)(i-1) alpha(i)delta(pi), in Omega,
epsilon(1 - t)partial derivative v/partial derivative v + tb(x)v = 0, on partial derivative Omega,
for epsilon small, where , a"broken vertical bar is a bounded, smooth domain in , I" := {p (1), ..., p (N) } aS, a"broken vertical bar is the set of singular sources, delta (p) denotes the Dirac mass at p, nu denotes unit outward normal vector to a,a"broken vertical bar and b(x) > 0 is a smooth function on a,a"broken vertical bar.

• 出版日期2012
• 单位浙江大学