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Multiplicity of solutions of Dirichlet problems associated with second-order equations in ℝ2

Part of: Boundary value problems

Published online by Cambridge University Press:  23 September 2009

F. Dalbono  and
C. Rebelo
F. Dalbono
Affiliation:
Faculdade de Ciências e Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Avenida Professor Gama Pinto 2, 1649003 Lisboa, Portugal; (francesca.dalbono@unito.it, (carlota@ptmat.fc.ul.pt)
C. Rebelo
Affiliation:
Faculdade de Ciências e Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Avenida Professor Gama Pinto 2, 1649003 Lisboa, Portugal; (francesca.dalbono@unito.it, (carlota@ptmat.fc.ul.pt)
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Abstract

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We study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinity.

Keywords

asymptotically linearmultiplicitysecond orderplanar systemsMorse index

MSC classification

Secondary: 34B15: Nonlinear boundary value problems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 3 , October 2009 , pp. 569 - 581
Copyright
Copyright © Edinburgh Mathematical Society 2009