Geodesic
Existence of Positive Solutions for a Three-Point Boundary Value Problem with Fractional $q$-Differences
Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 4
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In this paper, we consider the following nonlinear $q$-fractional three-point boundary value problem \begin{equation} (D_{q}^{\alpha}u)(t) + f(t,u(t))=0, \quad 0 t 1, \quad 2 \alpha 3,\\ u(0) = (D_qu)(0) = 0, \quad (D_qu)(1) = \beta (D_qu)(\eta), \end{equation} where $0\beta\eta^{\alpha-2}1$. By the properties of the Green function and the lower and upper solution method, some new existence to the above boundary value problem are established. As applications, examples are presented to illustrate the main results.
Classification : 26A33, 34B18, 34B27 
@article{BMMS_2014_37_4_a3,
     author = {Yueqiang Song},
     title = {Existence of {Positive} {Solutions} for a {Three-Point} {Boundary} {Value} {Problem}  with {Fractional} $q${-Differences}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2014},
     volume = {37},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2014_37_4_a3/}
}
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Yueqiang Song. Existence of Positive Solutions for a Three-Point Boundary Value Problem  with Fractional $q$-Differences. Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 4. http://geodesic.mathdoc.fr/item/BMMS_2014_37_4_a3/