On one-dimensional superlinear indefinite problems involving the ϕ -Laplacian

Let Ω : = (a, b) ⊂ R, m∈ L1(Ω) and ϕ: R→ R be an odd increasing homeomorphism. We consider the existence of positive solutions for problems of the form {-ϕ(u′)′=m(x)f(u)inΩ,u=0on∂Ω,where f: [0 , ∞) → [0 , ∞) is a continuous function which is, roughly speaking, superlinear with respect to ϕ. Our appr...

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Detalles Bibliográficos
Autores: Kaufmann, Uriel, Milne, Leandro Agustin
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/186138
Acceso en línea:http://hdl.handle.net/11336/186138
Access Level:acceso abierto
Palabra clave:ELLIPTIC ONE-DIMENSIONAL PROBLEMS
POSITIVE SOLUTIONS
Φ-LAPLACIAN
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:Let Ω : = (a, b) ⊂ R, m∈ L1(Ω) and ϕ: R→ R be an odd increasing homeomorphism. We consider the existence of positive solutions for problems of the form {-ϕ(u′)′=m(x)f(u)inΩ,u=0on∂Ω,where f: [0 , ∞) → [0 , ∞) is a continuous function which is, roughly speaking, superlinear with respect to ϕ. Our approach combines the Guo-Krasnoselskiĭ fixed-point theorem with some estimates on related nonlinear problems. We mention that our results are new even in the case m≥ 0.