Existence of positive solution for nonlinear fourth-order difference equations

Let T be an integer with T 5 and let T2 D f2; 3; : : : ; T g. We show the existence and multiplicity of positive solutions of the boundary value problem of nonlinear fourth-order difference equation 4u.t 􀀀 2/ 􀀀 f .t; u.t// D 0; t 2 T2; u.1/ D u.T C 1/ D 2u.0/ D 2u.T / D 0; where is a parameter, f V T2 T0;1/ ! T0;1/ is continuous.