Positive solutions for nonlinear singular third order boundary value problem

In this paper, we investigate the problem of existence of positive solutions for the nonlinear third order boundary value problem: u ‴ ( t ) + λ a ( t ) f ( u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ′ ( 0 ) = 0 , α u ′ ( 1 ) + β u ″ ( 1 ) = 0 , where λ is a positive parameter. By using Krasnoselskii’s fixed-point theorem of cone, we establish various results on the existence of positive solutions of the boundary value problem. various assumptions on a ( t ) and f ( u ( t ) ) , we give the intervals of the parameter λ which yield the existence of the positive solutions. An example is also given to illustrate the main results.