## Abstract and Applied Analysis

### Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional $({p}_{1},\dots ,{p}_{n})$-Laplacian Operator

Shapour Heidarkhani

#### 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 $-(|{u}_{i}^{\prime }{|}^{{p}_{i}-2}{u}_{i}^{\prime })\prime =\lambda {F}_{{u}_{i}}(x,{u}_{1},\dots ,{u}_{n})$ in $(0,1)$, ${u}_{i}(0)={\sum }_{j=1}^{m}{a}_{j}{u}_{i}({x}_{j})$, ${u}_{i}(1)={\sum }_{j=1}^{m}{b}_{j}{u}_{i}({x}_{j})$ for $1\le i\le n$, is established.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 389530, 15 pages.

Dates
First available in Project Euclid: 5 April 2013

https://projecteuclid.org/euclid.aaa/1365125171

Digital Object Identifier
doi:10.1155/2012/389530

Mathematical Reviews number (MathSciNet)
MR2903812

Zentralblatt MATH identifier
1241.35098

#### Citation

Heidarkhani, Shapour. Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional $({p}_{1},\dots ,{p}_{n})$ -Laplacian Operator. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 389530, 15 pages. doi:10.1155/2012/389530. https://projecteuclid.org/euclid.aaa/1365125171

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