Positive solutions of a singular nonlinear third order two-point boundary value problem

Abstract

In this paper some existence results of positive solutions for the following singular nonlinear third order two-point boundary value problem: x ‴ ( t ) − α ( t ) f ( t , x ( t ) ) = 0 , a < t < b , x ( a ) = x ( b ) = x ″ ( b ) = 0 are established, where α ∈ C ( ( a , b ) , [ 0 , + ∞ ) ) , f ∈ C ( [ a , b ] × ( 0 , + ∞ ) , [ 0 , + ∞ ) ) , α ( t ) may be singular at t = a , b and f ( t , x ) may be singular at x = 0 .