Existence results for singular three point bounda value problems on time scales

@inproceedings{Dacunha2004ExistenceRF,
title={Existence results for singular three point bounda value problems on time scales},
author={Jeffrey J. Dacunha and John M. Davis and Parmjeet K. Singh},
year={2004}
}

We prove the existence of a positive solution for the three point boundary value problem o scaleT given by y + f (x, y) = 0, x ∈ (0,1] ∩ T, y(0) = 0, y(p) = y(σ2(1)), wherep ∈ (0,1) ∩ T is fixed andf (x, y) is singular aty = 0 and possibly at x = 0, y = ∞. We do so by applying a fixed point theorem due to Gatica, Oliker, and Waltman [J. Differential Equa 79 (1989) 62] for mappings that are decreasing with respect to a cone. We also prove the an existence results for the related dynamic… CONTINUE READING