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

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)=δx(η),0<δη<1,0<η<1.The growth of f   with respect to x′x′ is allowed to be quadratic. We use some degree theory arguments to get the multiplicity result.