Abstract and Applied Analysis

Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions

Jiqiang Jiang, Lishan Liu, and Yonghong Wu

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Abstract

By means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term: u ′′ ( t ) = λ [ f ( t , u ( t ) ) q ( t ) ] , 0 < t < 1 , α u ( 0 ) β u ( 0 ) = 0 1 u ( s ) d ξ ( s ) , γ u ( 1 ) + δ u ( 1 ) = 0 1 u ( s ) d η ( s ), where λ > 0 is a parameter; f : ( 0 , 1 ) × ( 0 , ) [ 0 , ) is continuous; f ( t , x ) may be singular at t = 0 , t = 1, and x = 0 , and the perturbed term q : ( 0 , 1 ) [ 0 , + ) is Lebesgue integrable and may have finitely many singularities in ( 0 , 1 ) , which implies that the nonlinear term may change sign.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 696283, 21 pages.

Dates
First available in Project Euclid: 4 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365099937

Digital Object Identifier
doi:10.1155/2012/696283

Mathematical Reviews number (MathSciNet)
MR2947680

Zentralblatt MATH identifier
1251.34040

Citation

Jiang, Jiqiang; Liu, Lishan; Wu, Yonghong. Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 696283, 21 pages. doi:10.1155/2012/696283. https://projecteuclid.org/euclid.aaa/1365099937


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