Positive solutions of \(q\)-difference equation. (English) Zbl 1201.39003

Authors’ abstract: We investigate the existence of positive solutions of the \( q\)-difference equation \( -D_q^2u(t)=a(t) f(u(t))\) with some boundary conditions by applying a fixed point theorem in cones.


39A13 Difference equations, scaling (\(q\)-differences)
39A12 Discrete version of topics in analysis
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B27 Green’s functions for ordinary differential equations
39A22 Growth, boundedness, comparison of solutions to difference equations
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