Multiple Positive Solutions for Nonlinear Third-order Three-point Boundary-value Problems

This paper concerns the nonlinear third-order three-point boundary-value problem u′′′(t) + h(t)f(u(t)) = 0, t ∈ (0, 1), u(0) = u′(0) = 0, u′(1) = αu′(η), where 0 < η < 1 and 1 < α < 1 η . First, we establish the existence of at least three positive solutions by using the well-known Leggett-Williams fixed point theorem. And then, we prove the existence of at… CONTINUE READING