Glasgow Mathematical Journal

Research Article

EIGENVALUE PROBLEMS FOR SINGULAR ODES

DONAL O'REGANa1 and ALEKSANDRA ORPELa2

a1 Department of Mathematics, National University of Ireland, Galway, Ireland

a2 Faculty of Mathematics and Computer Science, University of Lodz, Poland e-mail: orpela@math.uni.lodz.pl

Abstract

We investigate eigenvalue intervals for the Dirichlet problem when the nonlinearity may be singular at t = 0 or t = 1. Our approach is based on variational methods and cover both sublinear and superlinear cases. We also study the continuous dependence of solutions on functional parameters.

(Received December 23 2009)

(Accepted June 28 2010)

(Online publication December 09 2010)

2010 Mathematics Subject Classification