Multi‐peak solutions for a class of degenerate elliptic equations

Article type: Research Article

Authors: Giacomini, Alessandro | Squassina, Marco

Affiliations: Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 4, 34014 Trieste, Italy E‐mail: giacomin@sissa.it | Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy E‐mail: marco.squassina@mate.polimi.it

Abstract: By means of a penalization argument due to del Pino and Felmer, we prove the existence of multi‐spike solutions for a class of quasilinear elliptic equations under natural growth conditions. Compared with the semilinear case some difficulties arise, mainly concerning the properties of the limit equation. The study of concentration of the solutions requires a somewhat involved analysis in which a Pucci–Serrin type identity plays an important role.

Keywords: multi‐peak solutions, degenerate elliptic equations, nonsmooth critical point theory, Palais–Smale condition, Pohožaev–Pucci–Serrin identity

Journal: Asymptotic Analysis, vol. 36, no. 2, pp. 115-147, 2003