Abstract and Applied Analysis
Volume 2004 (2004), Issue 11, Pages 957-979

Multiplicity results for asymmetric boundary value problems with indefinite weights

Francesca Dalbono

Dipartimento di Matematica, Facoltà di Scienze Matematiche Fisiche e Naturali, Università di Torino, Via Carlo Alberto, Torino 10 10123, Italy

Received 21 October 2003

Copyright © 2004 Francesca Dalbono. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the form u+f(t,u)=0, u(0)=u(T)=0. The nonlinearity is supposed to satisfy asymmetric, asymptotically linear assumptions involving indefinite weights. We first study some auxiliary half-linear, two-weighted problems for which an eigenvalue theory holds. Multiplicity is ensured by assumptions expressed in terms of weighted eigenvalues. The proof is developed in the framework of topological methods and is based on some relations between rotation numbers and weighted eigenvalues.