Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Bifurcation results for semilinear elliptic problems in RN

Marino Badialea1 and Alessio Pomponioa2

a1 Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy (badiale@dm.unito.it)

a2 SISSA, via Beirut 2–4, 34014 Trieste, Italy (pomponio@sissa.it)

Abstract

In this paper we obtain, for a semilinear elliptic problem in RN, families of solutions bifurcating from the bottom of the spectrum of −Δ. The problem is variational in nature and we apply a nonlinear reduction method that allows us to search for solutions as critical points of suitable functionals defined on finite-dimensional manifolds.

(Received January 22 2003)

(Accepted June 30 2003)