Existence of a positive solution to a first-order \(p\)-Laplacian BVP on a time scale (Q629308)

The author considers the first-order dynamic equation on a time scale \[ \phi_p(y^{\triangle}(t))= h(t) f(y^{\sigma}(t)), \quad a < t < b, \, t \in \mathbb{T}. \] He obtains a positive solution using a cone-theoretic theorem for the following types of non-local condititions: \[ u(a) = \psi(y), \quad y(a) = B_0(y^{\triangle}(b)), \quad y(a) = \left(y^{\triangle}(b)\right)^m, \] where \(\mathbb{T}\) is time scale, \(h\) is right-dense continuous, \(f\) is continuous, \(\psi\) is a functional, \(B_0\) is a continuous function with \(B_1x \leq B_0(x) \leq B_2x\), \(0 < m <1\).