Uniqueness of positive solutions for boundary value problems associated with indefinite ϕ-Laplacian-type equations
This paper provides a uniqueness result for positive solutions of the Neumann and periodic boundary value problems associated with the ϕ-Laplacian equation (ϕ(u′))′+a(t)g(u)=0,(\phi \left(u^{\prime} ))^{\prime} +a\left(t)g\left(u)=0, where ϕ is a homeomorphism with ϕ(0) = 0, a(t) is a stepwise indef...
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| Autores principales: | , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/5c429e8e95bf4301b19123687f3424c9 |
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| Sumario: | This paper provides a uniqueness result for positive solutions of the Neumann and periodic boundary value problems associated with the ϕ-Laplacian equation (ϕ(u′))′+a(t)g(u)=0,(\phi \left(u^{\prime} ))^{\prime} +a\left(t)g\left(u)=0, where ϕ is a homeomorphism with ϕ(0) = 0, a(t) is a stepwise indefinite weight and g(u) is a continuous function. When dealing with the p-Laplacian differential operator ϕ(s) = ∣s∣p−2
s with p > 1, and the nonlinear term g(u) = u
γ with γ∈R\gamma \in {\mathbb{R}}, we prove the existence of a unique positive solution when γ ∈ ]−∞\infty , (1 − 2p)/(p − 1)] ∪ ]p − 1, +∞\infty [. |
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