摘要：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 u Δ ∇ ( t ) = f ( t , u ( t ) , u Δ ( t ) ) , t ∈ [ 0 , 1 ] T , subject to one of the following multi-point boundary conditions: u ( 0 ) = ∑ i = 1 m α i u ( ξ i ) , u Δ ( 1 ) = 0 , and u ( 0 ) = ∑ i = 1 m α i u ( ξ i ) , u ( 1 ) = 0 , where T is a time scale such that 0 ∈ T , 1 ∈ T k , ξ i ∈ ( 0 , 1 ) ∩ T , i = 1 , 2 , … , m , f : [ 0 , 1 ] T × R 2 → R is continuous and satisfies the Carathéodory-type growth conditions. MSC:34B15, 39A10, 47G20.
关键词：multi-point BVP ; time scale ; resonance ; coincidence degree
