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15 December 2004 Multiplicity results for asymmetric boundary value problems with indefinite weights
Francesca Dalbono
Abstr. Appl. Anal. 2004(11): 957-979 (15 December 2004). DOI: 10.1155/S108533750440102X


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.


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Francesca Dalbono. "Multiplicity results for asymmetric boundary value problems with indefinite weights." Abstr. Appl. Anal. 2004 (11) 957 - 979, 15 December 2004.


Published: 15 December 2004
First available in Project Euclid: 30 December 2004

zbMATH: 1079.34007
MathSciNet: MR2130222
Digital Object Identifier: 10.1155/S108533750440102X

Primary: 34B15

Rights: Copyright © 2004 Hindawi

Vol.2004 • No. 11 • 15 December 2004
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