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.
A multiplicity result for singularly perturbed problems in topologically nontrivial domains
Giovanna Cerami;
2004-01-01
Abstract
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.File in questo prodotto:
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