Unbounded solutions for three-point boundary value problems with nonlinear boundary conditions on [0,+∞)[0,+∞)

The existence and multiplicity of unbounded solutions is investigated for second-order three-point differential equations with nonlinear boundary conditions on [0,+∞)[0,+∞), where the growth of the nonlinear term with respect to the third variable is allowed to be quadratic. By applying the techniques of unbounded upper and lower solutions and the topological degree theory, the existence of at least one solution and three solutions, respectively, is shown for the above problem. One example is worked out to indicate the applications of our main results.