Abstract and Applied Analysis

Abstract and Applied Analysis / 2004 / Article

Open Access

Volume 2004 |Article ID 537916 | 23 pages | https://doi.org/10.1155/S108533750440102X

Multiplicity results for asymmetric boundary value problems with indefinite weights

Received21 Oct 2003

Abstract

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.

Copyright © 2004 Hindawi Publishing Corporation. 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.

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