Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite Interval. (7th April 2013)

• Record Type: Journal Article
• Authors: Ma, Ruyun; Xie, Chunjie; Ahmed, Abubaker
• Other Names: Lan Kunquan Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-04-07
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/492026
• Languages: English
• ISSNs: 1085-3375

Abstract

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 ) = + ∞ .