Positive solutions for a class of semipositone singular boundary value problems on time scales (Q6566543)

In this paper, there is investigated the following semipositone singular boundary value problem\N\[\N\begin{gathered}\N-\left(\psi(t)y^\Delta\right)^\nabla(t)= q(t)f(t, y(t))+r(t),\quad t\in (\rho(c), \sigma(d)),\\\N\alpha y(\rho(c))-\beta \psi(\rho(c))y^\Delta(\rho(c))= 0,\\\N\gamma y(\sigma(d))+\delta \psi(d)y^\Delta(d)= 0,\N\end{gathered}\N\]\Nwhere \(\psi: [\rho(c), \sigma(d)]\to (0, \infty)\), \(f: [\rho(c), \sigma(d)]\times [0, \infty)\to [0, \infty)\) are continuous functions, \(q: (\rho(c), \sigma(d))\to (0, \infty)\) is a continuous function and \(r: (\rho(c), \sigma(d))\to (-\infty, \infty)\) is a Lebesgue \(\nabla\)-integrable function.\N\NThe authors give conditions for the parameters of the considered boundary value problem to ensure the existence of at least one positive solution and existence of at least two positive solutions.\N\NThe results in the paper are illustrated by examples.