Mixed interior and boundary nodal bubbling solutions for a sinh-Poisson equation

Juncheng Wei, Long Wei, Feng Zhou
2011 Pacific Journal of Mathematics  
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 where (ξ 1 , . . . , ξ 2(k+l) ) are critical points of some functional defined explicitly in terms of
more » ... licitly in terms of the associated Green function. J.
doi:10.2140/pjm.2011.250.225 fatcat:jpi4mdfhvbcaljjonjdi6a7chi