## Abstract and Applied Analysis

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

#### 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

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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