Triple positive solutions of a class of fourth-order two-point boundary value problems

In this paper, by using the Leggett–Williams fixed point theorem, we establish an existence criterion for triple positive solutions of the nonlinear fourth-order two-point boundary value problem { u ( 4 ) ( t ) = g ( t ) f ( t , u ( t ) , u ′ ( t ) ) , t ∈ ( 0 , 1 ) u ( 0 ) = u ′ ( 1 ) = u ″ ( 0 ) = u ‴ ( 1 ) = 0 . An example is also included to demonstrate the result we obtained.