## Abstract and Applied Analysis

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

### 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

#### 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