Abstract and Applied Analysis

Positive Solutions of the One-Dimensional p -Laplacian with Nonlinearity Defined on a Finite Interval

Ruyun Ma, Chunjie Xie, and Abubaker Ahmed

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Abstract

We use the quadrature method to show the existence and multiplicity of positive solutions of the boundary value problems involving one-dimensional p -Laplacian u t | p 2 u t + λ f u t = 0 , t 0,1 , u ( 0 ) = u ( 1 ) = 0 , where p ( 1,2 ] , λ ( 0 , ) is a parameter, f C 1 ( [ 0 , r ) , [ 0 , ) ) for some constant r > 0 , f ( s ) > 0 in ( 0 , r ) , and lim s r - ( r - s ) p - 1 f ( s ) = + .

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 492026, 6 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511829

Digital Object Identifier
doi:10.1155/2013/492026

Mathematical Reviews number (MathSciNet)
MR3039178

Zentralblatt MATH identifier
1276.34019

Citation

Ma, Ruyun; Xie, Chunjie; Ahmed, Abubaker. Positive Solutions of the One-Dimensional $p$ -Laplacian with Nonlinearity Defined on a Finite Interval. Abstr. Appl. Anal. 2013 (2013), Article ID 492026, 6 pages. doi:10.1155/2013/492026. https://projecteuclid.org/euclid.aaa/1393511829


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