Semilinear elliptic problems in unbounded domains with unbounded boundary

Article type: Research Article

Authors: Molle, Riccardo

Affiliations: Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica n° 1, 00133 Roma, Italy E‐mail: molle@mat.uniroma2.it

Abstract: This paper deals with a class of singularly perturbed nonlinear elliptic problems (Pε) with subcritical nonlinearity. The coefficient of the linear part is assumed to concentrate in a point of the domain, as ε→0, and the domain is supposed to be unbounded and with unbounded boundary. Domains that enlarge at infinity, and whose boundary flattens or shrinks at infinity, are considered. It is proved that in such domains problem (Pε) has at least 2 solutions.

Keywords: unbounded domains, unbounded boundary, concentrating potential, multiple solutions

Journal: Asymptotic Analysis, vol. 38, no. 3-4, pp. 293-307, 2004