Abstract and Applied Analysis

Existence of Positive Solutions for Third-Order m -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales

Fatma Tokmak and Ilkay Yaslan Karaca

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Abstract

A four-functional fixed point theorem and a generalization of Leggett-Williams fixed point theorem are used, respectively, to investigate the existence of at least one positive solution and at least three positive solutions for third-order m -point boundary value problem on time scales with an increasing homeomorphism and homomorphism, which generalizes the usual p -Laplacian operator. In particular, the nonlinear term f ( t , u ) is allowed to change sign. As an application, we also give some examples to demonstrate our results.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 506716, 15 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475975

Digital Object Identifier
doi:10.1155/2012/506716

Mathematical Reviews number (MathSciNet)
MR3004856

Zentralblatt MATH identifier
1261.34070

Citation

Tokmak, Fatma; Karaca, Ilkay Yaslan. Existence of Positive Solutions for Third-Order $m$ -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales. Abstr. Appl. Anal. 2012 (2012), Article ID 506716, 15 pages. doi:10.1155/2012/506716. https://projecteuclid.org/euclid.aaa/1364475975


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