On the number of nodal bubbling solutions to a sinh-Poisson equation

• Autores: Long Wei
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 35, Nº 1, 2009, págs. 291-326
• Idioma: inglés
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• Resumen

  • We show that for e>0 small, there exist arbitrarily many nodal solutions for the semi-linear equation Du + 2e2sinh u=0 posed on a bounded smooth domain in R2 with homogeneous Neumann boundary condition. More precisely, for e sufficiently small and any given positive integers L = 1, there exists a family of nodal solution ue that develops 2L boundary singularities and which with the property 2e2 So sinh u -> 4 p S2Lj=1 (-1) j-1d? j ,where ( ?1,···,? 2L) are critical points of some functional defined explicitly in terms of the associated Green's function. This solution has at least L+1 nodal domains. No assumption on the geometry, nor the topology of the domain is needed.