Existence of at least three solutions of a second-order three-point boundary value problem

Abstract

We study existence of at least three solutions in the presence of two lower and two upper solutions of some second-order nonlinear three-point boundary value problem of the type - x ″ = f ( t , x , x ′ ) , t ∈ I = [ 0 , 1 ] , x ( 0 ) = 0 , x ( 1 ) = δ x ( η ) , 0 < δ η < 1 , 0 < η < 1 . The growth of f with respect to x ′ is allowed to be quadratic. We use some degree theory arguments to get the multiplicity result.