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A note about positive solutions for an equation of Kirchhoff type |
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| Authors: | André LM Martinez Jair da Silva |
| Institution: | a Universidade Tecnológica Federal do Paraná, 86300-000 Cornélio Procópio, PR, Brazil b Colegiado de Matemática, Universidade Estadual do Oeste do Paraná, 85819-110 Cascavel, PR, Brazil c Departamento de Matemática, Universidade Federal do Mato Grosso do Sul, 79070-900 Campo Grande, MS, Brazil d Departamento de Matemática, Universidade Estadual de Maringá, 87020-900 Maringá, PR, Brazil |
| Abstract: | 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. |
| Keywords: | Krasnoselskii&rsquo s fixed point theorem Alternatives of Leray-Schauder Numerical solutions |
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