Existence and multiplicity results for some three-point boundary value problems Original Research Article

Using the method of upper and lower solutions and some degree theory arguments, we establish the existence of at least three solutions of some second-order nonlinear differential equations of the type View the MathML source−x″=f(t,x,x′),t∈I=[0,1] Turn MathJax on subject to nonlinear three-point boundary conditions View the MathML sourcex(0)=0,x′(1)=g(x(η)),0<η≤1. Turn MathJax on The growth of ff with respect to x′x′ is allowed to be quadratic.