Positive solutions for a class of boundary value problems on time scales

By obtaining intervals of the parameter λλ, this paper is concerned with the existence and nonexistence of positive solution of the second-order nonlinear dynamic equation on time scales −[p(t)xΔ(t)]∇+q(t)x(t)=λw(t)f(t,x),αx(ρ(a))−βx[Δ](ρ(a))=0,γx(b)+δx[Δ](b)=0 for t∈[a,b]⊂Tt∈[a,b]⊂T, where TT is a time scale, α≥0,γ≥0,β>0,δ>0α≥0,γ≥0,β>0,δ>0 with α+γ>0α+γ>0. The arguments are based upon fixed point theorems in a cone.