Positive Solutions of Singular Complementary Lidstone Boundary Value Problems. (2nd December 2010) - Agarwal Agarwal, Ravi P. Ravi P.; O'Regan O'Regan, Donal Donal; Staněk Staněk, Svatoslav Svatoslav
Abstract : We investigate the existence of positive solutions of singular problem ( - 1 ) m x ( 2 m + 1 ) = f ( t, x, …, x ( 2 m ) ), x ( 0 ) = 0, x ( 2 i - 1 ) ( 0 ) = x ( 2 i - 1 ) ( T ) = 0, 1 ≤ i ≤ m . Here, m ≥ 1 and the Carathéodory function f ( t, x 0, …, x 2 m ) may be singular in all its space variables x 0, …, x 2 m . The results are proved by regularization and sequential techniques. In limit processes, the Vitali convergence theorem is used.