Mixed interior and boundary nodal bubbling solutions for a sinh-Poisson equation
Juncheng Wei, Long Wei, Feng Zhou · Pacific Journal of Mathematics · 2011
We consider here the semilinear equation u + 2ε 2 sinh u = 0 posed on a bounded smooth domain in ޒ 2 with homogeneous Neumann boundary condition, where ε > 0 is a small parameter.We show that for any given nonnegative integers k and l with k + l ≥ 1, there exists a family of solutions u ε that develops 2k interior and 2l boundary singularities for ε sufficiently small, with the property that) are critical points of some functional defined explicitly in terms of the associated Green function.