SINGULAR DIRICHLET BOUNDARY VALUE PROBLEM FOR SECOND ORDER ODE

on his 70th birthday anniversary Abstract. This paper investigates the singular Dirichlet problem −u′ ′ = f(t, u, u′) , u(0) = 0, u(T) = 0, where f satisfies the Carathéodory conditions on the set (0, T) × R20 and R0 = R \ {0}. The function f(t, x, y) can have time singularities at t = 0 and t = T and space singularities at x = 0 and y = 0. The existence principle for the above problem is given and its application is presented here. The paper provides conditions which guarantee the existence of a solution which is positive on (0, T) and which has the absolutely continuous first derivative on [0, T]