Boundary Value Problems
We investigate the existence of positive solutions of singular problem (-1)mx(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 Carathéodory function f (t, x0,⋯, x2m) may be singular in all its space variables x0,⋯, x2m. The results are proved by regularization and sequential techniques. In limit processes, the Vitali convergence theorem is used.
Agarwal, R. P., O'Regan, D., & Staněk, S. (2010). Positive solutions of singular complementary lidstone boundary value problems. Boundary Value Problems, 2010(1), 368169.