## Abstract and Applied Analysis

### Positive Solutions for a Mixed-Order Three-Point Boundary Value Problem for $p$-Laplacian

Francisco J. Torres

#### Abstract

The author investigates the existence and multiplicity of positive solutions for boundary value problem of fractional differential equation with $p$-Laplacian operator. The main tool is fixed point index theory and Leggett-Williams fixed point theorem.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 912576, 8 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393512167

Digital Object Identifier
doi:10.1155/2013/912576

Mathematical Reviews number (MathSciNet)
MR3132573

Zentralblatt MATH identifier
07095483

#### Citation

Torres, Francisco J. Positive Solutions for a Mixed-Order Three-Point Boundary Value Problem for $p$ -Laplacian. Abstr. Appl. Anal. 2013 (2013), Article ID 912576, 8 pages. doi:10.1155/2013/912576. https://projecteuclid.org/euclid.aaa/1393512167

#### References

• R. Liang, J. Peng, and J. Shen, “Double positive solutions for a nonlinear four-point boundary value problem with a p-Lap-lacian operator,” Nonlinear Analysis: Theory, Methods & Applications, vol. 323, pp. 413–425, 2006.
• D. Zhao, H. Wang, and W. Ge, “Existence of triple positive solutions to a class of $p$-Laplacian boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 328, no. 2, pp. 972–983, 2007.
• G. Chai, “Positive solutions for boundary value problem of fractional differential equation with $p$-Laplacian operator,” Boundary Value Problems, vol. 2012, article 18, 2012.
• H. Su, Z. Wei, and B. Wang, “The existence of positive solutions for a nonlinear four-point singular boundary value problem with a $p$-Laplacian operator,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 66, no. 10, pp. 2204–2217, 2007.
• H. Su, “Positive solutions for $n$-order $m$-point $p$-Laplacian operator singular boundary value problems,” Applied Mathematics and Computation, vol. 199, no. 1, pp. 122–132, 2008.
• X. Tang, C. Yan, and Q. Liu, “Existence of solutions of two-point boundary value problems for fractional $p$-Laplace differential equations at resonance,” Journal of Applied Mathematics and Computing, vol. 41, no. 1-2, pp. 119–131, 2013.
• K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.
• D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, San Diego, Calif, USA, 1988.
• G. Chai, “Existence results for boundary value problems of non-linear fractional differential equations,” Computers & Mathematics with Applications, vol. 62, no. 5, pp. 2374–2382, 2011.
• F. J. Torres, “Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation,” Bulletin of the Iranian Mathematical Society, vol. 39, no. 2, pp. 307–323, 2013.
• R. W. Leggett and L. R. Williams, “Multiple positive fixed points of nonlinear operators on ordered Banach spaces,” Indiana University Mathematics Journal, vol. 28, no. 4, pp. 673–688, 1979.