Original Paper

Second order problems with functional conditions including Sturm–Liouville and multipoint conditions

Alberto Cabada

[email protected]

Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Galicia, Spain

Phone: +34 981 563100 Ext.13206, Fax: +34 981 597054

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Donal O'Regan,

Donal O'Regan

[email protected]

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

Phone: +352 (91)493091, Fax: +353(91) 750542

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Rodrigo L. Pouso,

Corresponding Author

Rodrigo L. Pouso

[email protected]

Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Galicia, Spain

Phone: +34 981 563100 Ext. 13166, Fax: +34 981 597054Search for more papers by this author

Alberto Cabada,

Alberto Cabada

[email protected]

Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Galicia, Spain

Phone: +34 981 563100 Ext.13206, Fax: +34 981 597054

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Donal O'Regan,

Donal O'Regan

[email protected]

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

Phone: +352 (91)493091, Fax: +353(91) 750542

Search for more papers by this author

Rodrigo L. Pouso,

Corresponding Author

Rodrigo L. Pouso

[email protected]

Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Galicia, Spain

Phone: +34 981 563100 Ext. 13166, Fax: +34 981 597054Search for more papers by this author

First published: 13 August 2008

https://doi.org/10.1002/mana.200510675

Citations: 21

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Abstract

In this paper we study the solvability of equations of the form

-(d/dt)φ (t, u, u (t), u ′(t)) = f (t, u, u (t), u ′(t)) for a.e. t ∈ I = [a, b ],

together with functional-boundary conditions which cover, amongst others, Sturm–Liouville and multipoint boundary data as particular cases. Our approach uses upper and lower solutions together with growth restrictions of Nagumo's type. An example is presented to show the applicability of the obtained results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Volume281, Issue9

September 2008

Pages 1254-1263

Second order problems with functional conditions including Sturm–Liouville and multipoint conditions

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Second order problems with functional conditions including Sturm–Liouville and multipoint conditions

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