Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional (𝑝1,…,𝑝𝑛)-Laplacian Operator

Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional (๐‘1,โ€ฆ,๐‘๐‘›)-Laplacian Operator

Employing a recent three critical points theorem due to Bonanno and Marano (2010), the existence of at least three solutions for the following multipoint boundary value system โˆ’(|๐‘ข๎…ž๐‘–|๐‘๐‘–โˆ’2๐‘ข๎…ž๐‘–)โ€ฒ=๐œ†๐น๐‘ข๐‘–(๐‘ฅ,๐‘ข1,โ€ฆ,๐‘ข๐‘›) in (0,1), ๐‘ข๐‘–โˆ‘(0)=๐‘š๐‘—=1๐‘Ž๐‘—๐‘ข๐‘–(๐‘ฅ๐‘—), ๐‘ข๐‘–โˆ‘(1)=๐‘š๐‘—=1๐‘๐‘—๐‘ข๐‘–(๐‘ฅ๐‘—) for 1โ‰ค๐‘–โ‰ค๐‘›, is established....

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Main Author: Shapour Heidarkhani
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/389530
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author Shapour Heidarkhani
author_facet Shapour Heidarkhani
author_sort Shapour Heidarkhani
collection DOAJ
description Employing a recent three critical points theorem due to Bonanno and Marano (2010), the existence of at least three solutions for the following multipoint boundary value system โˆ’(|๐‘ข๎…ž๐‘–|๐‘๐‘–โˆ’2๐‘ข๎…ž๐‘–)โ€ฒ=๐œ†๐น๐‘ข๐‘–(๐‘ฅ,๐‘ข1,โ€ฆ,๐‘ข๐‘›) in (0,1), ๐‘ข๐‘–โˆ‘(0)=๐‘š๐‘—=1๐‘Ž๐‘—๐‘ข๐‘–(๐‘ฅ๐‘—), ๐‘ข๐‘–โˆ‘(1)=๐‘š๐‘—=1๐‘๐‘—๐‘ข๐‘–(๐‘ฅ๐‘—) for 1โ‰ค๐‘–โ‰ค๐‘›, is established.
format Article
id doaj-art-47c6880eb5304813981f32a83d91ae87
institution Kabale University
issn 1085-3375
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language English
publishDate 2012-01-01
publisher Wiley
record_format Article
series Abstract and Applied Analysis
spelling doaj-art-47c6880eb5304813981f32a83d91ae872025-02-03T01:01:15ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/389530389530Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional (๐‘1,โ€ฆ,๐‘๐‘›)-Laplacian OperatorShapour Heidarkhani0Department of Mathematics, Faculty of Sciences, Razi University, Kermanshash 67149, IranEmploying a recent three critical points theorem due to Bonanno and Marano (2010), the existence of at least three solutions for the following multipoint boundary value system โˆ’(|๐‘ข๎…ž๐‘–|๐‘๐‘–โˆ’2๐‘ข๎…ž๐‘–)โ€ฒ=๐œ†๐น๐‘ข๐‘–(๐‘ฅ,๐‘ข1,โ€ฆ,๐‘ข๐‘›) in (0,1), ๐‘ข๐‘–โˆ‘(0)=๐‘š๐‘—=1๐‘Ž๐‘—๐‘ข๐‘–(๐‘ฅ๐‘—), ๐‘ข๐‘–โˆ‘(1)=๐‘š๐‘—=1๐‘๐‘—๐‘ข๐‘–(๐‘ฅ๐‘—) for 1โ‰ค๐‘–โ‰ค๐‘›, is established.http://dx.doi.org/10.1155/2012/389530
spellingShingle Shapour Heidarkhani
Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional (๐‘1,โ€ฆ,๐‘๐‘›)-Laplacian Operator
Abstract and Applied Analysis
title Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional (๐‘1,โ€ฆ,๐‘๐‘›)-Laplacian Operator
title_full Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional (๐‘1,โ€ฆ,๐‘๐‘›)-Laplacian Operator
title_fullStr Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional (๐‘1,โ€ฆ,๐‘๐‘›)-Laplacian Operator
title_full_unstemmed Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional (๐‘1,โ€ฆ,๐‘๐‘›)-Laplacian Operator
title_short Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional (๐‘1,โ€ฆ,๐‘๐‘›)-Laplacian Operator
title_sort multiple solutions for a class of multipoint boundary value systems driven by a one dimensional ๐‘1 ๐‘๐‘› laplacian operator
url http://dx.doi.org/10.1155/2012/389530
work_keys_str_mv AT shapourheidarkhani multiplesolutionsforaclassofmultipointboundaryvaluesystemsdrivenbyaonedimensionalp1pnlaplacianoperator

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