Abstract and Applied Analysis
Volume 2012 (2012), Article ID 389530, 15 pages
http://dx.doi.org/10.1155/2012/389530
Research Article

Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional ( 𝑝 1 , … , 𝑝 𝑛 ) -Laplacian Operator

Shapour Heidarkhani

Department of Mathematics, Faculty of Sciences, Razi University, Kermanshash 67149, Iran

Received 20 November 2011; Accepted 11 December 2011

Academic Editor: Kanishka Perera

Copyright © 2012 Shapour Heidarkhani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 − ( | 𝑢 𝑖 | 𝑝 𝑖 − 2 𝑢 𝑖 ) ′ = 𝜆 𝐹 𝑢 𝑖 ( 𝑥 , 𝑢 1 , … , 𝑢 𝑛 ) in ( 0 , 1 ) , 𝑢 𝑖 ∑ ( 0 ) = 𝑚 𝑗 = 1 𝑎 𝑗 𝑢 𝑖 ( 𝑥 𝑗 ) , 𝑢 𝑖 ∑ ( 1 ) = 𝑚 𝑗 = 1 𝑏 𝑗 𝑢 𝑖 ( 𝑥 𝑗 ) for 1 ≤ 𝑖 ≤ 𝑛 , is established.