Abstract and Applied Analysis

Multiple Positive Solutions of a Second Order Nonlinear Semipositone m -Point Boundary Value Problem on Time Scales

Chengjun Yuan and Yongming Liu

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Abstract

In this paper, we study a general second-order m -point boundary value problem for nonlinear singular dynamic equation on time scales u Δ ( t ) + a ( t ) u Δ ( t ) + b ( t ) u ( t ) + λ q ( t ) f ( t , u ( t ) ) = 0 , t ( 0,1 ) 𝕋 , u ( ρ ( 0 ) ) = 0 , u ( σ ( 1 ) ) = i = 1 m - 2 α i u ( η i ) . This paper shows the existence of multiple positive solutions if f is semipositone and superlinear. The arguments are based upon fixed-point theorems in a cone.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 261741, 19 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620779

Digital Object Identifier
doi:10.1155/2010/261741

Mathematical Reviews number (MathSciNet)
MR2726613

Zentralblatt MATH identifier
1236.34117

Citation

Yuan, Chengjun; Liu, Yongming. Multiple Positive Solutions of a Second Order Nonlinear Semipositone $m$ -Point Boundary Value Problem on Time Scales. Abstr. Appl. Anal. 2010 (2010), Article ID 261741, 19 pages. doi:10.1155/2010/261741. https://projecteuclid.org/euclid.aaa/1288620779


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