The problem -epsilon(2)Deltau + a(epsilon)(x)u = u(p-1) with zero Dirichlet boundary condition is considered in a nontrivial bounded domain Omega subset of R-N. Under the assumption that a, (x) greater than or equal to a(0) > 0 concentrates at a point of Omega as epsilon --> 0 and has a suitable behaviour at infinity and, moreover, that p > 2 and p < 2N/N-2 if N greater than or equal to 3, the existence of at least (catOmega) + 2 distinct positive solutions is proved.
|Titolo:||A multiplicity result for singularly perturbed problems in topologically nontrivial domains|
|Data di pubblicazione:||2004|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1515/ans-2004-0405|
|Appare nelle tipologie:||1.1 Articolo in rivista|