Multiple positive solutions for a singularly perturbed Dirichlet problem in "geometrically trivial" domains

Giovanna Cerami, Caterina Maniscalco

DOI: http://dx.doi.org/10.12775/TMNA.2002.004

Abstract


In this paper we consider the singularly perturbed Dirichlet problem
(P$_{\varepsilon}$), when the potential $a_{\varepsilon}(x)$, as $\varepsilon$ goes to
$0$, is concentrating round a point $x_0\in\Omega$.
Under suitable growth assumptions on $f$, we prove that (P$_{\varepsilon}$)
has at least three distinct solutions whatever $\Omega$ is and that at least
one solution is not a one-peak solution.

Keywords


Singularity perturbet elliptic problem; variational methods; critical point; Lusternik-Schnirelman theory; (LS)-category

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