## Abstract and Applied Analysis

### Positive Solutions for Third-Order $p$-Laplacian Functional Dynamic Equations on Time Scales

#### Abstract

We study the following third-order $p$-Laplacian functional dynamic equation on time scales: ${[{\mathrm{\Phi }}_{p}({u}^{\Delta \nabla }(t))]}^{\nabla }+a(t)f(u(t),u(\mu (t)))=0$, $t\in {(0,T)}_{\mathbf{T}}$,  $u(t)=\phi (t)$,  $t\in {[-r,0]}_{\mathbf{T}}$,  ${u}^{\Delta }(0)={u}^{\Delta \nabla }(T)=0$, and $u(T)+{B}_{0}({u}^{\Delta }(\eta ))=0$. By applying the Five-Functional Fixed Point Theorem, the existence criteria of three positive solutions are established.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 676052, 6 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412278108

Digital Object Identifier
doi:10.1155/2014/676052

Mathematical Reviews number (MathSciNet)
MR3248871

Zentralblatt MATH identifier
1343.34209

#### Citation

Guan, Wen; Wang, Da-Bin. Positive Solutions for Third-Order $p$ -Laplacian Functional Dynamic Equations on Time Scales. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 676052, 6 pages. doi:10.1155/2014/676052. https://projecteuclid.org/euclid.aaa/1412278108

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