Volume 36 • Number 4 • 2013   • Positive Solution for Fractional $q$-Difference Boundary Value Problems with $\phi$-Laplacian Operator Wengui Yang Abstract. In this paper, we investigate the existence of at least one positive solution for a class of fractional $q$-difference boundary value problems with $\phi$-Laplacian operator. The arguments mainly rely on the upper and lower solutions method as well as the Schauder's fixed point theorem. Nonlinear term may be singular at $t=0,1$ or $u=0$. Furthermore, two examples are presented to illustrate the main results. 2010 Mathematics Subject Classification:39A13, 34B18, 34A08 Full text: PDF