Positive solutions of singular complementary lidstone boundary value problems

Abstract

We investigate the existence of positive solutions of singular problem (-1)(m)x((2m+1)) = f(t, x, ..., x((2m))), x(0) = 0, x((2i-1))(0) = x((2i-1))(T) = 0, 1 <= i <= m. Here, m >= 1 and the Caratheodory function f(t, x(0), ..., x(2m)) may be singular in all its space variables x(0), ..., x(2m). The results are proved by regularization and sequential techniques. In limit processes, the Vitali convergence theorem is used.