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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Bibliographic Details
Main Author: Shapour Heidarkhani
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/389530
Description
Summary: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.
ISSN:1085-3375
1687-0409

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