Existence of a positive solution to a first-order pp-Laplacian BVP on a time scale

In this paper, we consider a first-order delta dynamic boundary value problem of the form ϕp(yΔ(t))=h(t)f(yσ(t))ϕp(yΔ(t))=h(t)f(yσ(t)), for t∈(a,b)Tt∈(a,b)T, subject to either the boundary condition y(a)=ψ(y)y(a)=ψ(y), the boundary condition y(a)=B0(yΔ(b))y(a)=B0(yΔ(b)), or the boundary condition y(a)=(yΔ(b))my(a)=(yΔ(b))m for m∈(0,1)m∈(0,1), where TT is a time scale, h:[a,b]T→[0,+∞) and f:[0,+∞)→[0,+∞) are continuous functions, ψ:Crd([a,σ(b)]T)→R is a given linear functional with the restriction that ψψ depends upon y(σ(b))y(σ(b)), and B0:R→R is a given continuous function. In this case, the function ϕp(⋅)ϕp(⋅) is the so-called one-dimensional pp-Laplacian. Our results here generalize recent results in the literature on this type of problem. We conclude with several numerical examples illustrating the results and the improvements and generalizations that they provide.