Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Variational perturbative methods and bifurcation of bound states from the essential spectrum*

Antonio Ambrosettia1 and Marino Badialea1

a1 Scuola Normale Superiore, Pisa, 56100, Italy

This paper consists of two main parts. The first deals with a perturbative method in critical point theory and can be seen as the generalisation and completion of some earlier results. The second part is concerned with applications of the abstract setup to the existence of bound states of a class of elliptic differential equations that branch off from the infimum of the essential spectrum.

(Received March 18 1997)

(Revised November 26 1997)


* Supported by M.U.R.S.T. National Project ‘Problemi non lineari…’ and by EEC contract no. ERBCHRXCT940494.