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:	Boscaggin Alberto, Feltrin Guglielmo, Zanolin Fabio
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	uniqueness indefinite weight positive solutions p-laplacian boundary value problems superlinear functions singular equations 34b15 34b16 34b18 34c25 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/5c429e8e95bf4301b19123687f3424c9
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spelling	oai:doaj.org-article:5c429e8e95bf4301b19123687f3424c92021-12-05T14:10:52ZUniqueness of positive solutions for boundary value problems associated with indefinite ϕ-Laplacian-type equations2391-545510.1515/math-2021-0003https://doaj.org/article/5c429e8e95bf4301b19123687f3424c92021-05-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0003https://doaj.org/toc/2391-5455This 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 [.Boscaggin AlbertoFeltrin GuglielmoZanolin FabioDe Gruyterarticleuniquenessindefinite weightpositive solutionsp-laplacianboundary value problemssuperlinear functionssingular equations34b1534b1634b1834c25MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 163-183 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	uniqueness indefinite weight positive solutions p-laplacian boundary value problems superlinear functions singular equations 34b15 34b16 34b18 34c25 Mathematics QA1-939
spellingShingle	uniqueness indefinite weight positive solutions p-laplacian boundary value problems superlinear functions singular equations 34b15 34b16 34b18 34c25 Mathematics QA1-939 Boscaggin Alberto Feltrin Guglielmo Zanolin Fabio Uniqueness of positive solutions for boundary value problems associated with indefinite ϕ-Laplacian-type equations
description	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 [.
format	article
author	Boscaggin Alberto Feltrin Guglielmo Zanolin Fabio
author_facet	Boscaggin Alberto Feltrin Guglielmo Zanolin Fabio
author_sort	Boscaggin Alberto
title	Uniqueness of positive solutions for boundary value problems associated with indefinite ϕ-Laplacian-type equations
title_short	Uniqueness of positive solutions for boundary value problems associated with indefinite ϕ-Laplacian-type equations
title_full	Uniqueness of positive solutions for boundary value problems associated with indefinite ϕ-Laplacian-type equations
title_fullStr	Uniqueness of positive solutions for boundary value problems associated with indefinite ϕ-Laplacian-type equations
title_full_unstemmed	Uniqueness of positive solutions for boundary value problems associated with indefinite ϕ-Laplacian-type equations
title_sort	uniqueness of positive solutions for boundary value problems associated with indefinite ϕ-laplacian-type equations
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/5c429e8e95bf4301b19123687f3424c9
work_keys_str_mv	AT boscagginalberto uniquenessofpositivesolutionsforboundaryvalueproblemsassociatedwithindefinitephlaplaciantypeequations AT feltringuglielmo uniquenessofpositivesolutionsforboundaryvalueproblemsassociatedwithindefinitephlaplaciantypeequations AT zanolinfabio uniquenessofpositivesolutionsforboundaryvalueproblemsassociatedwithindefinitephlaplaciantypeequations
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Uniqueness of positive solutions for boundary value problems associated with indefinite ϕ-Laplacian-type equations

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