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
Multiple positive solutions for a singularly perturbed Dirichlet problem in "geometrically trivial" domains / Cerami, Giovanna; Maniscalco, Caterina. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - STAMPA. - 19:1(2002), pp. 63-76. [10.12775/TMNA.2002.004]
Multiple positive solutions for a singularly perturbed Dirichlet problem in "geometrically trivial" domains
Giovanna Cerami;
2002-01-01
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 solutionI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
