Multiple positive solutions for a singularly perturbed Dirichlet problem in "geometrically trivial" domains
Keywords
Singularity perturbet elliptic problem, variational methods, critical point, Lusternik-Schnirelman theory, (LS)-categoryAbstract
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.Downloads
Published
2002-03-01
How to Cite
1.
CERAMI, Giovanna and MANISCALCO, Caterina. Multiple positive solutions for a singularly perturbed Dirichlet problem in "geometrically trivial" domains. Topological Methods in Nonlinear Analysis. Online. 1 March 2002. Vol. 19, no. 1, pp. 63 - 76. [Accessed 28 March 2024].
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