Abstract
In this paper we are concerned with the following third-order two-point boundary value problem on time scale T u Δ Δ Δ ( t ) + f ( t , u ( t ) , u Δ Δ ( t ) ) = 0 , t ∈ [ a , ρ ( b ) ] , u ( a ) = A , u ( σ 2 ( b ) ) = B , u Δ Δ ( a ) = C . Some existence criteria of solution and positive solution are established by using Leray–Schauder fixed point theorem and our main conditions are local. An example is also included to illustrate the importance of the results obtained.
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