Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter

This paper is concerned with the following second-order three-point boundary value problem u ''(t) + beta(2)u (t) + lambda q (t) f (t, u (t)) = 0 t epsilon (0, 1), u (0) = 0, u(1) = delta u(eta), where beta epsilon (0, pi/2), delta > 0, eta epsilon (0,1), and lambda is a positive parameter. First, Green's function for the associated linear boundary value problem is constructed, and then some useful properties of Green's function are obtained. Finally, existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values of lambda by means of the fixed point index theory.