Abstract
By applying the coincidence degree theorem due to Mawhin, we show the existence of at least one solution to the nonlinear second-order differential equation subject to one of the following multi-point boundary conditions: and where is a time scale such that , , , , is continuous and satisfies the Caratheodory-type growth conditions. MSC:34B15, 39A10, 47G20.
Highlights
We assume that the reader is familiar with some notations and basic results for dynamic equations on time scales
There is much current activity focused on dynamic equations on time scales, and a good deal of this activity is devoted to boundary value problems
Motivated by the papers mentioned above, in this paper, by making use of the coincidence degree theory due to Mawhin [ ], we study u ∇ (t) = f t, u(t), u (t), t ∈ [, a]T, ( . )
Summary
We assume that the reader is familiar with some notations and basic results for dynamic equations on time scales. We study two new multi-point BVPs on time scales at resonance, which have rarely been considered, and we need to overcome some new difficulties.
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