Construction of Nodal Bubbling Solutions for the Weighted Sinh-Poisson Equation

Abstract

We consider the weighted sinh-Poisson equation in , on , where is a small parameter, , and is a unit ball in . By a constructive way, we prove that for any positive integer , there exists a nodal bubbling solution which concentrates at the origin and the other -points , , such that as , , where and is an odd integer with , or is an even integer. The same techniques lead also to a more general result on general domains