SOME EXISTENCE RESULTS OF SEMILINEAR SINGULARLY PERTURBED NONLOCAL BOUNDARY VALUE PROBLEMS

By standard barrier solution method associated with Schauder fixed point theorem, we establish an existence theory for nonlinear second order nonlinear multi-point boundary value problem $(1.3)$, $(1.4)$. Through the pervious existence theorem, we mainly work out some asymptotic behaviors of solutions for semilinear singularly perturbed three-point boundary value problem $(1.1)$, $(1.2)$. Barrier solutions will be constructed explicitly when the boundary or interior layers occur, respectively.