Positive Solutions for a Class of Fourth-order Singular BVPs on the Positive Half-line

In this work, we are concerned with the existence and multiplicity of positive solutions for the singular fourth-order boundary value problem on the half-line x((4)) (t) - eta x ''(t) + lambda x(t) = phi(t) f(t, x(t), x'(t), x ''(t), x '''(t)), t is an element of I = (0,+infinity), x(0) = x ''(0) = 0, x(+infinity) = x ''(+infinity) = 0 where f is an element of C (R+ x I x R-3, R+) and eta, lambda are real positive constants such that eta(2) > 4 lambda By using the fixed point index theory on cones in appropriate Banach spaces, we obtained existence results of single and multiple positive solutions.