×

Nontrivial solutions for fractional \(q\)-difference boundary value problems. (English) Zbl 1207.39010

Electron. J. Qual. Theory Differ. Equ. 2010, Paper No. 70, 10 p. (2010); corrigendum ibid. 2019, Paper No. 44, 2 p. (2019).
Summary: We investigate the existence of nontrivial solutions to the nonlinear \(q\)-fractional boundary value problem
\[ \begin{cases} (D_q^\alpha y)(x)=-f(x,y(x)),\quad 0<x<1,\\ y(0)=0=y(1),\end{cases} \]
by applying a fixed point theorem in cones.

MSC:

39A13 Difference equations, scaling (\(q\)-differences)
39A12 Discrete version of topics in analysis
34A08 Fractional ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI EuDML EMIS