Abstract :
Let T be a time scale such that 0,T ∈ T, β, γ 0 and 0 < η < ρ(T). We consider the following p-
Laplacian three-point boundary problem on time scales
ϕp u (t) ∇ +λh(t)f u(t) = 0, t∈ (0,T ),
u(0) − βu (0) = γu (η), u (T ) = 0,
where p >1, λ>0, h ∈ Cld((0,T ), [0,∞)) and f ∈ C([0,∞), (0,∞)). Some sufficient conditions for the
nonexistence and existence of at least one or two positive solutions for the boundary value problem are
established. In doing so the usual restriction that f0 = limu→0+
f (u)
ϕp(u) and f∞ = limu→∞
f (u)
ϕp(u) exist is
removed. An example is also given to illustrate the main results.
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