A note about positive solutions for an equation of Kirchhoff type

A nonlinear boundary value problem related to an equation of Kirchhoff is considered. The existence of positive solutions is proved through alternative Leray–Schauder’s type combined with Krasnoselskii’s fixed point theorem. Numerical methods are presented and a result of local convergence is establ...

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Bibliographic Details
Published in:Applied mathematics and computation 2011-11, Vol.218 (5), p.2082-2090
Main Authors: Martinez, André L.M., Castelani, Emerson V., Silva, Jair da, Shirabayashi, Wesley V.I.
Format: Article
Language:English
Subjects:
Alternatives of Leray–Schauder
Boundary value problems
Computation
Convergence
Existence theorems
Krasnoselskii’s fixed point theorem
Mathematical analysis
Mathematical models
Nonlinearity
Numerical analysis
Numerical solutions
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Summary:A nonlinear boundary value problem related to an equation of Kirchhoff is considered. The existence of positive solutions is proved through alternative Leray–Schauder’s type combined with Krasnoselskii’s fixed point theorem. Numerical methods are presented and a result of local convergence is established.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.07.025